Question 1

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-160° 
A) $340 ^ { \circ }$ and $- 20 ^ { \circ }$

B) $520^{\circ} \text { and }-200^{\circ}$

C) $520 ^ { \circ }$ and $- 200 ^ { \circ }$

D) $340 ^ { \circ }$ and $- 20 ^ { \circ }$

Accepted Answer

B

Question 2

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-
A) Obtuse, equilateral
B) Acute, isosceles
C) Obtuse, scalene
D) Acute, scalene

Accepted Answer

B

Question 3

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure.
-csc (° °)and cot (° °)
A)positive and positive
B)negative and negative
C)positive and negative
D)negative and positive

Accepted Answer

D

Question 4

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-csc ϴ, given that sin ϴ = -0.0214
A)23.365
B)46.729
C)-23.365
D)-46.729

Accepted Answer

The answer of Use the appropriate identity to find the...

Question 5

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
-C 
A) $\mathrm { C }$
B) $R$
C) $\mathrm { T }$
D) $S$

Accepted Answer

The answer of The triangles are similar. Find the angle...

Question 6

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-(4, -2) 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch an angle in standard position such...

Question 7

The triangles are similar. Find the missing side, angle or value of the variable.
-

$a = 14$
$b = 21$
$c = 10$
$d = 15$
$e = 20$

A) $x = 28$
B) $x = 26$
C) $x = 20$
D) $x = 35$

Accepted Answer

The answer of The triangles are similar. Find the missing...

Question 8

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-(-2, 5) 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch an angle in standard position such...

Question 9

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-98° 
A) $98 ^ { \circ } + n \cdot 720 ^ { \circ }$
B) $98 ^ { \circ } + n \cdot 360 ^ { \circ }$
C) $98 ^ { \circ } + \mathrm { n } \cdot 90 ^ { \circ }$
D) $98 ^ { \circ } + \mathrm { n } \cdot 180 ^ { \circ }$

Accepted Answer

Two angles are coterminal if they differ by a multiple of $360^\circ$, which is the angle for a complete circle. Therefore, adding $360^\circ$ multiplied by any integer $n$ to the given angle $98^\circ$ generates all angles coterminal with $98^\circ$.

Question 10

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the
indicated trig function for .
-(18, 24); Find csc ϴ. 
A) $\frac { 4 } { 3 }$
B) $\frac { 3 } { 4 }$
C) $\frac { 5 } { 3 }$
D) $\frac { 5 } { 4 }$

Accepted Answer

The answer of Suppose that is in standard position and...

Question 11

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle.
-B 
A) $\mathrm { C }$
B) $T$
C) $S$
D) $R$

Accepted Answer

The answer of The triangles are similar. Find the angle...

Question 12

Identify the quadrant for the angle satisfying the following conditions.
-cot ϴ > 0 and sin ϴ < 0
A)Quadrant I
B)Quadrant IV
C)Quadrant III
D)Quadrant II

Accepted Answer

The answer of Identify the quadrant for the angle satisfying...

Question 13

Find the measure of the third angle of a triangle if the measures of the other two angles are given.
-27° and 101°
A)128°
B)232°
C)38°
D)52°

Accepted Answer

The answer of Find the measure of the third angle...

Question 14

Solve the problem. Round answers to the nearest tenth if necessary.
-A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.
A)75.5 m
B)18.7 m
C)17.2 m
D)77.0 m

Accepted Answer

The height of the tree can be found using similar triangles. The ratio of the height of the statue to its shadow (37/75) is equal to the ratio of the height of the tree to its shadow. Let $ h $ be the height of the tree in meters. Thus, $ \frac{37}{75} = \frac{h}{38} $. Solving for $ h $, we get $ h = \frac{37 \times 38}{75} \approx 18.7 $ meters.

Question 15

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
-tan(n · 180°)
A)0
B)1
C)Undefined
D)-1

Accepted Answer

The tangent of any integer multiple of 180° is 0 because tan(180°) = 0 and the tangent function has a period of 180°.

Question 16

Find the measure of each angle in the problem.
-Complementary angles with measures 3x and 6x - 18 degrees
A)66° and 114°
B)12° and 78°
C)36° and 54°
D)38° and 52°

Accepted Answer

Complementary angles add up to 90 degrees. Setting up the equation 3x + (6x - 18) = 90, combining like terms gives 9x - 18 = 90. Adding 18 to both sides gives 9x = 108, and dividing by 9 gives x = 12. Substituting x = 12 into the expressions for the angles gives 3(12) = 36 degrees and 6(12) - 18 = 72 - 18 = 54 degrees.

Question 17

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal
side of .
-(3, -6) 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch an angle in standard position such...

Question 18

Perform the calculation.
-279°39´ + 139°38´
A)18°77´
B)18°17´
C)419°17´
D)419°77´

Accepted Answer

Adding the degrees and minutes separately: 279° + 139° = 418° and 39´ + 38´ = 77´. Since 60 minutes make a degree, 77´ is equal to 1° 17´. Therefore, 418° + 1° = 419°, and the minutes are 17´, making the answer 419°17´.

Question 19

Find the exact value of the expression.
-B 
A) $C$
B) $T$
C) $R$
D) $\mathrm { S }$

Accepted Answer

The answer of Find the exact value of the expression.
-B...

Question 20

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene.
-
A) Acute, equilateral
B) Obtuse, isosceles
C) Obtuse, equilateral
D) Acute, scalene

Accepted Answer

The answer of Classify the triangle as acute, right, or...

Quiz 1: Trigonometric Functions

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -160°

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -csc (° °) and cot (° °)

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. -csc ϴ, given that sin ϴ = -0.0214

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -C $The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -C A) \mathrm { C } B) R C) \mathrm { T } D) S$

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(4, -2)

The triangles are similar. Find the missing side, angle or value of the variable. - $a = 14$ $b = 21$ $c = 10$ $d = 15$ $e = 20$

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(-2, 5)

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -98°

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . -(18, 24) ; Find csc ϴ.

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -B $The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -B A) \mathrm { C } B) T C) S D) R$

Identify the quadrant for the angle satisfying the following conditions. -cot ϴ > 0 and sin ϴ < 0

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -27° and 101°

Solve the problem. Round answers to the nearest tenth if necessary. -A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. -tan(n · 180°)

Find the measure of each angle in the problem. -Complementary angles with measures 3x and 6x - 18 degrees

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(3, -6)

Perform the calculation. -279°39´ + 139°38´

Find the exact value of the expression. -B $Find the exact value of the expression. -B A) C B) T C) R D) \mathrm { S }$

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Quiz 1: Trigonometric Functions

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -160°

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

Determine the signs of the given trigonometric functions of an angle in standard position with the given measure. -csc (° °) and cot (° °)

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. -csc ϴ, given that sin ϴ = -0.0214

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -C

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(4, -2)

The triangles are similar. Find the missing side, angle or value of the variable. - a=14a = 14a=14 b=21b = 21b=21 c=10c = 10c=10 d=15d = 15d=15 e=20e = 20e=20

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(-2, 5)

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -98°

Suppose that is in standard position and the given point is on the terminal side of . Give the exact value of the indicated trig function for . -(18, 24) ; Find csc ϴ.

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -B

Identify the quadrant for the angle satisfying the following conditions. -cot ϴ > 0 and sin ϴ < 0

Find the measure of the third angle of a triangle if the measures of the other two angles are given. -27° and 101°

Solve the problem. Round answers to the nearest tenth if necessary. -A tree casts a shadow 38 m long. At the same time, the shadow cast by a 37-centimeter-tall statue is 75 cm long. Find the height of the tree.

If n is an integer, n · 180° represents an integer multiple of 180°, and (2n + 1) · 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. -tan(n · 180°)

Find the measure of each angle in the problem. -Complementary angles with measures 3x and 6x - 18 degrees

Sketch an angle in standard position such that has the least positive measure and the given point is on the terminal side of . -(3, -6)

Perform the calculation. -279°39´ + 139°38´

Find the exact value of the expression. -B

Classify the triangle as acute, right, or obtuse and classify it as equilateral, isosceles, or scalene. -

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -C $The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -C A) \mathrm { C } B) R C) \mathrm { T } D) S$

The triangles are similar. Find the missing side, angle or value of the variable. - $a = 14$ $b = 21$ $c = 10$ $d = 15$ $e = 20$

The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -B $The triangles are similar. Find the angle or side that corresponds to the given angle or side in the other triangle. -B A) \mathrm { C } B) T C) S D) R$

Find the exact value of the expression. -B $Find the exact value of the expression. -B A) C B) T C) R D) \mathrm { S }$