Deck 5: Trigonometric Functions: Unit Circle Approach

ملء الشاشة (f)
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سؤال
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> is the point Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> on the unit circle. Find the terminal point determined by
(a) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(b) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(c) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(d) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> .
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سؤال
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV.<div style=padding-top: 35px> on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV.<div style=padding-top: 35px> - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV.<div style=padding-top: 35px> is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV.<div style=padding-top: 35px> and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV.<div style=padding-top: 35px> is in quadrant IV.
سؤال
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> is the point Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> on the unit circle. Find the terminal point determined by
(a) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(b) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(c) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(d) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> .
سؤال
On the unit circle, determine which quadrant contains the terminal point of the arc whose length is On the unit circle, determine which quadrant contains the terminal point of the arc whose length is   .<div style=padding-top: 35px> .
سؤال
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> determined by Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> .
سؤال
Find the terminal point Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> .
سؤال
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> is the point Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> . Find the terminal point determined by each of the following:
(a) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(b) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(c) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> ,
(d) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   .<div style=padding-top: 35px> .
سؤال
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> determined by Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> .
سؤال
Find the terminal point Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> .
سؤال
On the unit circle, determine which quadrant contains the terminal point of the arc whose length is On the unit circle, determine which quadrant contains the terminal point of the arc whose length is   .<div style=padding-top: 35px> .
سؤال
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> determined by Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> .
سؤال
Find the terminal point Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   .<div style=padding-top: 35px> .
سؤال
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> is in quadrant III.
سؤال
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> determined by Find the reference number and the terminal point   determined by   .<div style=padding-top: 35px> .
سؤال
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I.<div style=padding-top: 35px> on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I.<div style=padding-top: 35px> - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I.<div style=padding-top: 35px> is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I.<div style=padding-top: 35px> and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I.<div style=padding-top: 35px> is in quadrant I.
سؤال
Find the reference number for Find the reference number for   .<div style=padding-top: 35px> .
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III.<div style=padding-top: 35px> is in quadrant III.
سؤال
Show that Show that   is on the unit circle.<div style=padding-top: 35px> is on the unit circle.
سؤال
Show that Show that   is on the unit circle.<div style=padding-top: 35px> is on the unit circle.
سؤال
Find the approximate value of Find the approximate value of   using a calculator.<div style=padding-top: 35px> using a calculator.
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Given that Given that   and   , find the quadrant in which the terminal point determined by   lies.<div style=padding-top: 35px> and Given that   and   , find the quadrant in which the terminal point determined by   lies.<div style=padding-top: 35px> , find the quadrant in which the terminal point determined by Given that   and   , find the quadrant in which the terminal point determined by   lies.<div style=padding-top: 35px> lies.
سؤال
Find the sign of Find the sign of   if the terminal point determined by   is in quadrant II.<div style=padding-top: 35px> if the terminal point determined by Find the sign of   if the terminal point determined by   is in quadrant II.<div style=padding-top: 35px> is in quadrant II.
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
If the terminal point determined by If the terminal point determined by   is   , find   ,   and   .<div style=padding-top: 35px> is If the terminal point determined by   is   , find   ,   and   .<div style=padding-top: 35px> , find If the terminal point determined by   is   , find   ,   and   .<div style=padding-top: 35px> , If the terminal point determined by   is   , find   ,   and   .<div style=padding-top: 35px> and If the terminal point determined by   is   , find   ,   and   .<div style=padding-top: 35px> .
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
Find the values of the trigonometric functions of Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> given that Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> and Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> .
سؤال
If the terminal point determined by If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> is If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> , find If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> , If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> and If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> .
سؤال
Find the values of the trigonometric functions of Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> given that Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> and Find the values of the trigonometric functions of   given that   and   .<div style=padding-top: 35px> .
سؤال
Find the approximate value of Find the approximate value of   using a calculator.<div style=padding-top: 35px> using a calculator.
سؤال
If the terminal point determined by If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> is If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> , find If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> , If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> and If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> If the terminal point determined by   is   , find     ,     and     .<div style=padding-top: 35px> .
سؤال
Find the approximate value of Find the approximate value of   using a calculator.<div style=padding-top: 35px> using a calculator.
سؤال
Find the approximate value of Find the approximate value of   using a calculator.<div style=padding-top: 35px> using a calculator.
سؤال
Find the exact value of Find the exact value of   and   .<div style=padding-top: 35px> and Find the exact value of   and   .<div style=padding-top: 35px> .
سؤال
Find the sign of Find the sign of   if the terminal point determined by   is in quadrant IV.<div style=padding-top: 35px> if the terminal point determined by Find the sign of   if the terminal point determined by   is in quadrant IV.<div style=padding-top: 35px> is in quadrant IV.
سؤال
Indicate if the function Indicate if the function   is even, odd or neither.<div style=padding-top: 35px> is even, odd or neither.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find all solutions of the equation Find all solutions of the equation   that lie in the interval   . State each answer correct to two decimal places.<div style=padding-top: 35px> that lie in the interval Find all solutions of the equation   that lie in the interval   . State each answer correct to two decimal places.<div style=padding-top: 35px> . State each answer correct to two decimal places.
سؤال
Graph the three functions Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> , Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> , and Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> on a common screen. Explain how the graphs are related.
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Find the amplitude, period, and phase shift of the function Find the amplitude, period, and phase shift of the function   , and sketch its graph for one complete period.<div style=padding-top: 35px> , and sketch its graph for one complete period.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Graph the three functions Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> , Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> , and Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related.<div style=padding-top: 35px> on a common screen. Explain how the graphs are related.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the maximum and minimum values of the function Find the maximum and minimum values of the function   .<div style=padding-top: 35px> .
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Sketch the graph of Sketch the graph of   .<div style=padding-top: 35px> .
سؤال
Find the exact value of each expression, if it is defined.
(a)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)  <div style=padding-top: 35px> ( b)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)  <div style=padding-top: 35px>
(c)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)  <div style=padding-top: 35px>
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the exact value of each expression, if it is defined. Find the exact value of each expression, if it is defined.      <div style=padding-top: 35px> Find the exact value of each expression, if it is defined.      <div style=padding-top: 35px> Find the exact value of each expression, if it is defined.      <div style=padding-top: 35px>
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the period of the function Find the period of the function   and sketch its graph.<div style=padding-top: 35px> and sketch its graph.
سؤال
Find the approximate value of Find the approximate value of   correct to   decimal places.<div style=padding-top: 35px> correct to Find the approximate value of   correct to   decimal places.<div style=padding-top: 35px> decimal places.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
سؤال
Find the value of Find the value of   if it is defined.<div style=padding-top: 35px> if it is defined.
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Deck 5: Trigonometric Functions: Unit Circle Approach
1
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . is the point Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . on the unit circle. Find the terminal point determined by
(a) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(b) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(c) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(d) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . .
(a) (a)   (b)   (c)   (d)
(b) (a)   (b)   (c)   (d)
(c) (a)   (b)   (c)   (d)
(d) (a)   (b)   (c)   (d)
2
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV. on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV. - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV. is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV. and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant IV. is in quadrant IV.
  is in quadrant IV, so   is negative.   . So   .  is in quadrant IV, so   is in quadrant IV, so   is negative.   . So   .  is negative.   is in quadrant IV, so   is negative.   . So   .  . So   is in quadrant IV, so   is negative.   . So   .  . 
3
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . is the point Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . on the unit circle. Find the terminal point determined by
(a) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(b) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(c) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . ,
(d) Suppose that the terminal point determined by   is the point   on the unit circle. Find the terminal point determined by (a)   , (b)   , (c)   , (d)   . .
(a) (a)   (b)   (c)   (d)
(b) (a)   (b)   (c)   (d)
(c) (a)   (b)   (c)   (d)
(d) (a)   (b)   (c)   (d)
4
On the unit circle, determine which quadrant contains the terminal point of the arc whose length is On the unit circle, determine which quadrant contains the terminal point of the arc whose length is   . .
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5
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   . determined by Find the reference number and the terminal point   determined by   . .
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6
Find the terminal point Find the terminal point   on the unit circle determined by the value   . on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   . .
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7
Suppose that the terminal point determined by Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . is the point Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . . Find the terminal point determined by each of the following:
(a) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . ,
(b) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . ,
(c) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . ,
(d) Suppose that the terminal point determined by   is the point   . Find the terminal point determined by each of the following: (a)   , (b)   , (c)   , (d)   . .
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k this deck
8
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   . determined by Find the reference number and the terminal point   determined by   . .
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9
Find the terminal point Find the terminal point   on the unit circle determined by the value   . on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   . .
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10
On the unit circle, determine which quadrant contains the terminal point of the arc whose length is On the unit circle, determine which quadrant contains the terminal point of the arc whose length is   . .
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11
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   . determined by Find the reference number and the terminal point   determined by   . .
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12
Find the terminal point Find the terminal point   on the unit circle determined by the value   . on the unit circle determined by the value Find the terminal point   on the unit circle determined by the value   . .
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13
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. is in quadrant III.
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k this deck
14
Find the reference number and the terminal point Find the reference number and the terminal point   determined by   . determined by Find the reference number and the terminal point   determined by   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
15
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I. on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I. - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I. is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I. and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant I. is in quadrant I.
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16
Find the reference number for Find the reference number for   . .
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17
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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18
Find Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. on the unit circle, given that the Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. - coordinate of Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. is Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. and Find   on the unit circle, given that the   - coordinate of   is   and   is in quadrant III. is in quadrant III.
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19
Show that Show that   is on the unit circle. is on the unit circle.
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20
Show that Show that   is on the unit circle. is on the unit circle.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
21
Find the approximate value of Find the approximate value of   using a calculator. using a calculator.
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22
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
23
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
24
Sketch the graph of Sketch the graph of   . .
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25
Sketch the graph of Sketch the graph of   . .
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26
Given that Given that   and   , find the quadrant in which the terminal point determined by   lies. and Given that   and   , find the quadrant in which the terminal point determined by   lies. , find the quadrant in which the terminal point determined by Given that   and   , find the quadrant in which the terminal point determined by   lies. lies.
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27
Find the sign of Find the sign of   if the terminal point determined by   is in quadrant II. if the terminal point determined by Find the sign of   if the terminal point determined by   is in quadrant II. is in quadrant II.
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28
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
29
If the terminal point determined by If the terminal point determined by   is   , find   ,   and   . is If the terminal point determined by   is   , find   ,   and   . , find If the terminal point determined by   is   , find   ,   and   . , If the terminal point determined by   is   , find   ,   and   . and If the terminal point determined by   is   , find   ,   and   . .
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30
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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31
Find the values of the trigonometric functions of Find the values of the trigonometric functions of   given that   and   . given that Find the values of the trigonometric functions of   given that   and   . and Find the values of the trigonometric functions of   given that   and   . .
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32
If the terminal point determined by If the terminal point determined by   is   , find     ,     and     . is If the terminal point determined by   is   , find     ,     and     . , find If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . , If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . and If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . .
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33
Find the values of the trigonometric functions of Find the values of the trigonometric functions of   given that   and   . given that Find the values of the trigonometric functions of   given that   and   . and Find the values of the trigonometric functions of   given that   and   . .
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34
Find the approximate value of Find the approximate value of   using a calculator. using a calculator.
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35
If the terminal point determined by If the terminal point determined by   is   , find     ,     and     . is If the terminal point determined by   is   , find     ,     and     . , find If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . , If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . and If the terminal point determined by   is   , find     ,     and     . If the terminal point determined by   is   , find     ,     and     . .
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36
Find the approximate value of Find the approximate value of   using a calculator. using a calculator.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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37
Find the approximate value of Find the approximate value of   using a calculator. using a calculator.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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38
Find the exact value of Find the exact value of   and   . and Find the exact value of   and   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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39
Find the sign of Find the sign of   if the terminal point determined by   is in quadrant IV. if the terminal point determined by Find the sign of   if the terminal point determined by   is in quadrant IV. is in quadrant IV.
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40
Indicate if the function Indicate if the function   is even, odd or neither. is even, odd or neither.
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41
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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42
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph. and sketch its graph.
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43
Sketch the graph of Sketch the graph of   . .
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44
Sketch the graph of Sketch the graph of   . .
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45
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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46
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph. and sketch its graph.
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47
Find all solutions of the equation Find all solutions of the equation   that lie in the interval   . State each answer correct to two decimal places. that lie in the interval Find all solutions of the equation   that lie in the interval   . State each answer correct to two decimal places. . State each answer correct to two decimal places.
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48
Graph the three functions Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. , Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. , and Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. on a common screen. Explain how the graphs are related.
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49
Sketch the graph of Sketch the graph of   . .
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50
Find the amplitude, period, and phase shift of the function Find the amplitude, period, and phase shift of the function   , and sketch its graph for one complete period. , and sketch its graph for one complete period.
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51
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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52
Graph the three functions Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. , Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. , and Graph the three functions   ,   , and   on a common screen. Explain how the graphs are related. on a common screen. Explain how the graphs are related.
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53
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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54
Find the maximum and minimum values of the function Find the maximum and minimum values of the function   . .
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55
Sketch the graph of Sketch the graph of   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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56
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
57
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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58
Sketch the graph of Sketch the graph of   . .
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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59
Find the amplitude, period and phase shift of Find the amplitude, period and phase shift of   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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60
Sketch the graph of Sketch the graph of   . .
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61
Find the exact value of each expression, if it is defined.
(a)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)  ( b)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)
(c)
Find the exact value of each expression, if it is defined. (a)   ( b)   (c)
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62
Find the value of Find the value of   if it is defined. if it is defined.
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63
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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64
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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65
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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66
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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67
Find the exact value of each expression, if it is defined. Find the exact value of each expression, if it is defined.      Find the exact value of each expression, if it is defined.      Find the exact value of each expression, if it is defined.
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68
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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69
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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70
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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71
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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72
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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73
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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74
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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75
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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k this deck
76
Find the period of the function Find the period of the function   and sketch its graph. and sketch its graph.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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77
Find the approximate value of Find the approximate value of   correct to   decimal places. correct to Find the approximate value of   correct to   decimal places. decimal places.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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78
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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79
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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80
Find the value of Find the value of   if it is defined. if it is defined.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.
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افتح القفل للوصول البطاقات البالغ عددها 100 في هذه المجموعة.