Question 1

Use your graphing calculator to graph the pair of functions for   together on a single coordinate system. (Make sure your calculator is set to radian mode.)  ​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

B

Question 2

Sketch the graph of y = csc  x between x = -4 π  and x  =  4 π  by extending the graph for x between 0 and 2 π .  ​  
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

First, we need to plot the graph of y = csc x for x between 0 and 2π. Recall that csc x = 1/sin x, so the graph of y = csc x will have vertical asymptotes at x = 0, π, and 2π where sin x = 0.

We can plot some key points on the graph:
- When x = 0, csc x is undefined because sin x = 0 in the denominator. 
- When x = π/2, sin x = 1 so csc x = 1/sin x = 1. 
- When x = π, sin x = 0 again so csc x is undefined. 
- When x = 3π/2, sin x = -1 so csc x = -1. 
- When x = 2π, sin x = 0 again so csc x is undefined.

Using these key points and the fact that the graph repeats every 2π, we can sketch the full graph of y = csc x from x = 0 to x = 4π as shown in choice B. The graph has vertical asymptotes at x = 0, π, 2π, 3π, and 4π, and it passes through the points (π/2, 1) and (3π/2, -1).

Question 3

If  , find sin(- θ ).

Accepted Answer

The answer of If  , find sin(- θ )....

Question 4

Find all values of x for which the following is true. sin x = 1
​
A)kπ
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of x for which...

Question 5

Evaluate without using a calculator.  ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Evaluate without using a calculator.  ​
A)...

Question 6

Find the algebraic expression that is equal to cos (180° -  θ ). ​
A) 
B)-sin  θ
C)sin  θ
D)-cos  θ
E)cos  θ

Accepted Answer

Using the formula cos (180° - θ) = -cos θ, the algebraic expression that is equal to cos (180° - θ) is -cos θ. Therefore, the best choice is D.

Question 7

Use your graphing calculator to graph the family of functions for   together on a single coordinate system. (Make sure your calculator is set to radian mode.) y = A sin  x for A = 1, 4, 6
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Use your graphing calculator to graph the...

Question 8

Use your graphing calculator to graph the pair of functions for  . (Make sure your calculator is set to radian mode.) y = cos  Bx for B = 1, 3
​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of Use your graphing calculator to graph the...

Question 9

Prove the identity. 
cos(- β )csc( - β )tan( - β )= 1

Accepted Answer

The answer of Prove the identity. 
cos(- β )csc( -...

Question 10

Find all values of x for which the following is true: sec x = -1
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of x for which...

Question 11

Match between columns
                        Premises: kπ

Accepted Answer

The Answer of tan x and cot x is...

Question 12

Match between columns
                        Premises: <img src="https://d2lvgg3v3hfg70.cloudfront.net/TBX9354/11ebf5ef_bb88_1b20_95d1_75aee0c87c63_TBX9354_11.jpg" alt=" " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

The Answer of cot x and tan x is...

Question 13

Sketch the graph of y = cos  x  between x = -4 π  and x  =  4 π  by extending the graph for x between 0 and 2 π .  ​
A)​ 
B)​ 
C)​

Accepted Answer

The answer of Sketch the graph of y = cos ...

Question 14

Prove the identity.

Accepted Answer

The answer of Prove the identity. ...

Question 15

Use your graphing calculator to graph the pair of functions for   together on a single coordinate system. (Make sure your calculator is set to radian mode.)  ​
A)​ 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The pair of functions are:
$$f(x) = \sin(x)$$
$$g(x) = -\sin(2x)$$

To graph both functions on a single coordinate system:

1. Press the "y=" button on your calculator.
2. Enter "sin(x)" in the first equation (Y1).
3. Enter "-sin(2x)" in the second equation (Y2).
4. Press the "graph" button.

You will see that the graphs intersect at many points, but they do not overlap each other completely. The best choice is A because it shows the intersection points clearly.

Question 16

Find the algebraic expression that is equal to sec θ - cos(- θ ). A) B) C) D)tan ² θ E)

Accepted Answer

The answer of Find the algebraic expression that is equal...

Question 17

If  , find cos (- θ ). ​
A) 
B) 
C)04
D) 
E)

Accepted Answer

The answer of If  , find cos (- θ )....

Question 18

Find all values of x for which the following is true. sec x is undefined.
​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find all values of x for which...

Question 19

Match between columns
                        Premises: <img src="https://d2lvgg3v3hfg70.cloudfront.net/TBX9354/11ebf5ef_bb87_f40f_95d1_4317f4a0b756_TBX9354_11.jpg" alt=" " class="answers-bank-image d-inline" rel="preload" >

Accepted Answer

The Answer of sec x = -1 and cot x is...

Question 20

Find the algebraic expression that is equal to sin(- θ )sec( - θ )cot( - θ ). ​
A)1
B)sec( - θ )
C)csc( - θ )
D)cos( - θ )
E)sin( - θ )

Accepted Answer

The answer of Find the algebraic expression that is equal...

Quiz 4: Graphing and Inverse Functions

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.)

Sketch the graph of y = csc x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π .

If , find sin(- θ ).

Find all values of x for which the following is true. sin x = 1

Evaluate without using a calculator.

Find the algebraic expression that is equal to cos (180° - θ ) .

Use your graphing calculator to graph the family of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.) y = A sin x for A = 1, 4, 6

Use your graphing calculator to graph the pair of functions for . (Make sure your calculator is set to radian mode.) y = cos Bx for B = 1, 3

Prove the identity. cos(- β )csc( - β )tan( - β )= 1

Find all values of x for which the following is true: sec x = -1

Match each value of x below with the letter of the corresponding function.

Match each value of x below with the letter of the corresponding function.

Sketch the graph of y = cos x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π .

Prove the identity.

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.)

Find the algebraic expression that is equal to sec θ - cos(- θ ) .

If , find cos (- θ ) .

Find all values of x for which the following is true. sec x is undefined.

Match each value of x below with the letter of the corresponding equation.

Find the algebraic expression that is equal to sin(- θ ) sec( - θ ) cot( - θ ) .

Quiz 4: Graphing and Inverse Functions

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.) ​

Sketch the graph of y = csc x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π . ​ ​

If , find sin(- θ ).

Find all values of x for which the following is true. sin x = 1 ​

Evaluate without using a calculator. ​

Find the algebraic expression that is equal to cos (180° - θ ) . ​

Use your graphing calculator to graph the family of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.) y = A sin x for A = 1, 4, 6 ​

Use your graphing calculator to graph the pair of functions for . (Make sure your calculator is set to radian mode.) y = cos Bx for B = 1, 3 ​

Prove the identity. cos(- β )csc( - β )tan( - β )= 1

Find all values of x for which the following is true: sec x = -1 ​

Match each value of x below with the letter of the corresponding function.

Match each value of x below with the letter of the corresponding function.

Sketch the graph of y = cos x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π . ​

Prove the identity.

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.) ​

Find the algebraic expression that is equal to sec θ - cos(- θ ) . ​

If , find cos (- θ ) . ​

Find all values of x for which the following is true. sec x is undefined. ​

Match each value of x below with the letter of the corresponding equation.

Find the algebraic expression that is equal to sin(- θ ) sec( - θ ) cot( - θ ) . ​

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.)

Sketch the graph of y = csc x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π .

Find all values of x for which the following is true. sin x = 1

Evaluate without using a calculator.

Find the algebraic expression that is equal to cos (180° - θ ) .

Use your graphing calculator to graph the family of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.) y = A sin x for A = 1, 4, 6

Use your graphing calculator to graph the pair of functions for . (Make sure your calculator is set to radian mode.) y = cos Bx for B = 1, 3

Find all values of x for which the following is true: sec x = -1

Sketch the graph of y = cos x between x = -4 π and x = 4 π by extending the graph for x between 0 and 2 π .

Use your graphing calculator to graph the pair of functions for together on a single coordinate system. (Make sure your calculator is set to radian mode.)

Find the algebraic expression that is equal to sec θ - cos(- θ ) .

If , find cos (- θ ) .

Find all values of x for which the following is true. sec x is undefined.

Find the algebraic expression that is equal to sin(- θ ) sec( - θ ) cot( - θ ) .