Question 1

Find the exact value of the expression if θ = 45°. Do not use a calculator.
-$$f ( \theta ) = \cos \theta \quad \text { Find } f ( \theta ) \text {. }$$

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 3 }$ 
B)  $\sqrt { 2 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 }$ 
A)  $\frac { \sqrt { 3 } } { 3 }$ 
B)  $\sqrt { 2 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  $- \frac { \sqrt { 2 } } { 2 }$

Question 2

Use transformations to graph the function.
-$y=\cos x-1$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 3

Solve the problem.
-$\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\cot \theta$

Accepted Answer

A)  $\frac { 4 \sqrt { 15 } } { 15 }$ 
B)  4 
C)  $\frac { \sqrt { 15 } } { 15 }$ 
D)  $\sqrt { 15 }$ 
A)  $\frac { 4 \sqrt { 15 } } { 15 }$ 
B)  4 
C)  $\frac { \sqrt { 15 } } { 15 }$ 
D)  $\sqrt { 15 }$

Question 4

Find the exact value of the indicated trigonometric function of $\theta$
-$\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$

Accepted Answer

A)  $- \frac { 20 } { 21 }$ 
B)  $- \frac { 21 \sqrt { 2 } } { 4 }$ 
C)  $- \frac { 21 } { 20 }$ 
D)  $\frac { 29 } { 20 }$ 
A)  $- \frac { 20 } { 21 }$ 
B)  $- \frac { 21 \sqrt { 2 } } { 4 }$ 
C)  $- \frac { 21 } { 20 }$ 
D)  $\frac { 29 } { 20 }$

Question 5

Use transformations to graph the function.
-$y=\cos \left(\frac{\pi}{2} x\right)$

A)

Accepted Answer

B)

C) 
  
D)

B)

C) 
  
D)

Question 6

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
-$\mathrm { r } = 8.8 \text { inches, } \theta = 60 ^ { \circ } , \mathrm { s } =$ ?

Accepted Answer

A)  9.5 in. 
B)  9.2 in. 
C)  9.3 in. 
D)  9.4 in. 
A)  9.5 in. 
B)  9.2 in. 
C)  9.3 in. 
D)  9.4 in.

Question 7

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\tan \frac { 17 \pi } { 4 }$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  $\sqrt { 3 }$ 
D)  $\frac { \sqrt { 3 } } { 3 }$ 
A)  1 
B)  $- 1$ 
C)  $\sqrt { 3 }$ 
D)  $\frac { \sqrt { 3 } } { 3 }$

Question 8

Find the exact value of the indicated trigonometric function of $\theta$
-$\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

Accepted Answer

A)  $\frac { 9 \sqrt { 181 } } { 181 }$ 
B)  $\frac { \sqrt { 145 } } { 8 }$ 
C)  $- \frac { \sqrt { 181 } } { 9 }$ 
D)  $- \frac { 9 \sqrt { 145 } } { 145 }$ 
A)  $\frac { 9 \sqrt { 181 } } { 181 }$ 
B)  $\frac { \sqrt { 145 } } { 8 }$ 
C)  $- \frac { \sqrt { 181 } } { 9 }$ 
D)  $- \frac { 9 \sqrt { 145 } } { 145 }$

Question 9

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of
the indicated trigonometric function of t.
-$\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin \mathrm { t }$.

Accepted Answer

A)  $\frac { \sqrt { 77 } } { 2 }$ 
B)  $\frac { \sqrt { 77 } } { 9 }$ 
C)  $\frac { 2 \sqrt { 77 } } { 77 }$ 
D)  $\frac { 2 } { 9 }$ 
A)  $\frac { \sqrt { 77 } } { 2 }$ 
B)  $\frac { \sqrt { 77 } } { 9 }$ 
C)  $\frac { 2 \sqrt { 77 } } { 77 }$ 
D)  $\frac { 2 } { 9 }$

Question 10

Convert the angle in radians to degrees.
-$$- \frac { 7 \pi } { 10 }$$

Accepted Answer

A)  $- 125 ^ { \circ }$ 
B)  $- 126 ^ { \circ }$ 
C)  $- 127 ^ { \circ }$ 
D)  $- 128 ^ { \circ }$ 
A)  $- 125 ^ { \circ }$ 
B)  $- 126 ^ { \circ }$ 
C)  $- 127 ^ { \circ }$ 
D)  $- 128 ^ { \circ }$

Question 11

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\cot \left( - \frac { \pi } { 4 } \right)$

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 3 }$ 
B)  $- \sqrt { 3 }$ 
C)  1 
D)  $- 1$ 
A)  $- \frac { \sqrt { 3 } } { 3 }$ 
B)  $- \sqrt { 3 }$ 
C)  1 
D)  $- 1$

Question 12

Graph the function.
-$y=-6 \csc \left(x+\frac{\pi}{4}\right)$
 
 A)

Accepted Answer

B) 
  
C) 
  
D) 
  
B) 
  
C) 
  
D)

Question 13

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$\mathrm { f } ( \theta ) = \cos \theta \quad$ Find $[ \mathrm { f } ( \theta ) ] ^ { 2 }$.

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 4 }$

Question 14

Solve the problem.
-For the equation $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Accepted Answer

A)  (i) $\frac { 1 } { 2 }$
(ii) $\pi$
(iii) $\pi$ 
B)  (i) $\frac { 1 } { 2 }$
(ii) $\frac { \pi } { 2 }$
(iii) $\pi$ 
C)  (i) 2
(ii) $\pi$
(iii) $\pi$ 
D)  (i) 2
(ii) $2 \pi$
(iii) $2 \pi$ 
A)  (i) $\frac { 1 } { 2 }$
(ii) $\pi$
(iii) $\pi$ 
B)  (i) $\frac { 1 } { 2 }$
(ii) $\frac { \pi } { 2 }$
(iii) $\pi$ 
C)  (i) 2
(ii) $\pi$
(iii) $\pi$ 
D)  (i) 2
(ii) $2 \pi$
(iii) $2 \pi$

Question 15

Convert the angle in radians to degrees.
-$$\frac { \pi } { 5 }$$

Accepted Answer

A)  $45 ^ { \circ }$ 
B)  $4 ^ { \circ }$ 
C)  $1 ^ { \circ }$ 
D)  $45 \pi ^ { \circ }$ 
A)  $45 ^ { \circ }$ 
B)  $4 ^ { \circ }$ 
C)  $1 ^ { \circ }$ 
D)  $45 \pi ^ { \circ }$

Question 16

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of
the indicated trigonometric function of t.
-$\left( - \frac { \sqrt { 21 } } { 5 } , - \frac { 2 } { 5 } \right)$ Find cot $\mathrm { t }$

Accepted Answer

A)  $- \frac { \sqrt { 21 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $- \frac { 2 \sqrt { 21 } } { 21 }$ 
D)  $\frac { \sqrt { 21 } } { 5 }$ 
A)  $- \frac { \sqrt { 21 } } { 2 }$ 
B)  $\frac { \sqrt { 21 } } { 2 }$ 
C)  $- \frac { 2 \sqrt { 21 } } { 21 }$ 
D)  $\frac { \sqrt { 21 } } { 5 }$

Question 17

Find an equation for the graph.
-  A) $y = 3 \sin ( 4 \pi x )$

Accepted Answer

B)  $y = 3 \sin \left( \frac { \pi } { 4 } x \right)$ 
C)  $y = 4 \sin ( 3 \pi x )$ 
D)  $y = 4 \sin \left( \frac { \pi } { 3 } x \right)$ 
B)  $y = 3 \sin \left( \frac { \pi } { 4 } x \right)$ 
C)  $y = 4 \sin ( 3 \pi x )$ 
D)  $y = 4 \sin \left( \frac { \pi } { 3 } x \right)$

Question 18

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$
-$- 105 ^ { \circ }$

Accepted Answer

A)  $- \frac { 7 \pi } { 12 }$ 
B)  $- \frac { 6 \pi } { 11 }$ 
C)  $- \frac { 12 \pi } { 7 }$ 
D)  $- \frac { 8 \pi } { 13 }$ 
A)  $- \frac { 7 \pi } { 12 }$ 
B)  $- \frac { 6 \pi } { 11 }$ 
C)  $- \frac { 12 \pi } { 7 }$ 
D)  $- \frac { 8 \pi } { 13 }$

Question 19

Solve the problem.
-What is the range of the sine function?

Accepted Answer

A)  all real numbers greater than or equal to 1 or less than or equal to -1 
B)  all real numbers greater than or equal to 0 
C)  all real numbers 
D)  all real numbers from -1 to 1, inclusive 
A)  all real numbers greater than or equal to 1 or less than or equal to -1 
B)  all real numbers greater than or equal to 0 
C)  all real numbers 
D)  all real numbers from -1 to 1, inclusive

Question 20

Without graphing the function, determine its amplitude or period as requested.
-$y = 4 \cos \frac { 1 } { 3 } x \quad$ Find the period.

Accepted Answer

A)  4 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $6 \pi$ 
D)  $\frac { \pi } { 3 }$ 
A)  4 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $6 \pi$ 
D)  $\frac { \pi } { 3 }$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad \text { Find } f ( \theta ) \text {. }$

Solve the problem. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\cot \theta$

Find the exact value of the indicated trigonometric function of $\theta$ - $\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = 8.8 \text { inches, } \theta = 60 ^ { \circ } , \mathrm { s } =$ ?

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\tan \frac { 17 \pi } { 4 }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( \frac { 2 } { 9 } , \frac { \sqrt { 77 } } { 9 } \right) \quad$ Find $\sin \mathrm { t }$ .

Convert the angle in radians to degrees. - $- \frac { 7 \pi } { 10 }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\cot \left( - \frac { \pi } { 4 } \right)$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $\mathrm { f } ( \theta ) = \cos \theta \quad$ Find $[ \mathrm { f } ( \theta ) ] ^ { 2 }$ .

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Convert the angle in radians to degrees. - $\frac { \pi } { 5 }$

In the problem, t is a real number and P = (x, y) is the point on the unit circle that corresponds to t. Find the exact value of the indicated trigonometric function of t. - $\left( - \frac { \sqrt { 21 } } { 5 } , - \frac { 2 } { 5 } \right)$ Find cot $\mathrm { t }$

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ - $- 105 ^ { \circ }$

Solve the problem. -What is the range of the sine function?

Without graphing the function, determine its amplitude or period as requested. - $y = 4 \cos \frac { 1 } { 3 } x \quad$ Find the period.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 5: Trigonometric Functions

Find the exact value of the expression if θ = 45°. Do not use a calculator. - f(θ)=cos⁡θ Find f(θ). f ( \theta ) = \cos \theta \quad \text { Find } f ( \theta ) \text {. }f(θ)=cosθ Find f(θ).

Use transformations to graph the function. - y=cos⁡x−1y=\cos x-1y=cosx−1 A) B) C) D)

Solve the problem. - sin⁡θ=14,cos⁡θ=154\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quadsinθ=41​,cosθ=415​​ Find cot⁡θ\cot \thetacotθ

Find the exact value of the indicated trigonometric function of θ\thetaθ - cos⁡θ=2129,3π2<θ<2π\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quadcosθ=2921​,23π​<θ<2π Find cot⁡θ\cot \thetacotθ

Use transformations to graph the function. - y=cos⁡(π2x)y=\cos \left(\frac{\pi}{2} x\right)y=cos(2π​x) A) B) C) D)

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - r=8.8 inches, θ=60∘,s=\mathrm { r } = 8.8 \text { inches, } \theta = 60 ^ { \circ } , \mathrm { s } =r=8.8 inches, θ=60∘,s= ?

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - tan⁡17π4\tan \frac { 17 \pi } { 4 }tan417π​

Find the exact value of the indicated trigonometric function of θ\thetaθ - cot⁡θ=−98,cos⁡θ<0\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quadcotθ=−89​,cosθ<0 Find csc⁡θ\csc \thetacscθ

Convert the angle in radians to degrees. - −7π10- \frac { 7 \pi } { 10 }−107π​

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - cot⁡(−π4)\cot \left( - \frac { \pi } { 4 } \right)cot(−4π​)

Graph the function. - y=−6csc⁡(x+π4)y=-6 \csc \left(x+\frac{\pi}{4}\right)y=−6csc(x+4π​) A) B) C) D)

Find the exact value of the expression if θ = 30°. Do not use a calculator. - f(θ)=cos⁡θ\mathrm { f } ( \theta ) = \cos \theta \quadf(θ)=cosθ Find [f(θ)]2[ \mathrm { f } ( \theta ) ] ^ { 2 }[f(θ)]2 .

Solve the problem. -For the equation y=−12cos⁡(2x−2πy = - \frac { 1 } { 2 } \cos ( 2 x - 2 \piy=−21​cos(2x−2π ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Convert the angle in radians to degrees. - π5\frac { \pi } { 5 }5π​

Convert the angle in degrees to radians. Express the answer as multiple of π.\pi .π. - −105∘- 105 ^ { \circ }−105∘

Solve the problem. -What is the range of the sine function?

Without graphing the function, determine its amplitude or period as requested. - y=4cos⁡13xy = 4 \cos \frac { 1 } { 3 } x \quady=4cos31​x Find the period.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad \text { Find } f ( \theta ) \text {. }$

Solve the problem. - $\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\cot \theta$

Find the exact value of the indicated trigonometric function of $\theta$ - $\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = 8.8 \text { inches, } \theta = 60 ^ { \circ } , \mathrm { s } =$ ?

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\tan \frac { 17 \pi } { 4 }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\cot \theta = - \frac { 9 } { 8 } , \quad \cos \theta < 0 \quad$ Find $\csc \theta$

Convert the angle in radians to degrees. - $- \frac { 7 \pi } { 10 }$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\cot \left( - \frac { \pi } { 4 } \right)$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $\mathrm { f } ( \theta ) = \cos \theta \quad$ Find $[ \mathrm { f } ( \theta ) ] ^ { 2 }$ .

Solve the problem. -For the equation $y = - \frac { 1 } { 2 } \cos ( 2 x - 2 \pi$ ), identify (i) the amplitude, (ii) the phase shift, and (iii) the period.

Convert the angle in radians to degrees. - $\frac { \pi } { 5 }$

Convert the angle in degrees to radians. Express the answer as multiple of $\pi .$ - $- 105 ^ { \circ }$

Without graphing the function, determine its amplitude or period as requested. - $y = 4 \cos \frac { 1 } { 3 } x \quad$ Find the period.