Question 1

Solve the problem.
-If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 4$, find the exact value of $f ( a ) + f ( a + \pi ) + f ( a + 3 \pi )$.

Accepted Answer

A)  $- 4$ 
B)  $- 12 + 4 \pi$ 
C)  $- 12$ 
D)  undefined 
A)  $- 4$ 
B)  $- 12 + 4 \pi$ 
C)  $- 12$ 
D)  undefined

Question 2

Draw the angle.
-$$\frac { 2 \pi } { 3 }$$

Accepted Answer

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

Question 3

Use transformations to graph the function.
-$y=5 \cos (\pi-x)$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 4

Find the area A. Round the answer to three decimal places.
-

Accepted Answer

A)  $1.963 \mathrm {~m} ^ { 2 }$ 
B)  $9.817 \mathrm {~m} ^ { 2 }$ 
C)  $6.25 \mathrm {~m} ^ { 2 }$ 
D)  $19.635 \mathrm {~m} ^ { 2 }$ 
A)  $1.963 \mathrm {~m} ^ { 2 }$ 
B)  $9.817 \mathrm {~m} ^ { 2 }$ 
C)  $6.25 \mathrm {~m} ^ { 2 }$ 
D)  $19.635 \mathrm {~m} ^ { 2 }$

Question 5

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If
necessary, round the answer to two decimal places.
-$r = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $A =$ ?

Accepted Answer

A)  $176.8 \mathrm {~cm} ^ { 2 }$ 
B)  $56.3 \mathrm {~cm} ^ { 2 }$ 
C)  $4.5 \mathrm {~cm} ^ { 2 }$ 
D)  $353.6 \mathrm {~cm} ^ { 2 }$ 
A)  $176.8 \mathrm {~cm} ^ { 2 }$ 
B)  $56.3 \mathrm {~cm} ^ { 2 }$ 
C)  $4.5 \mathrm {~cm} ^ { 2 }$ 
D)  $353.6 \mathrm {~cm} ^ { 2 }$

Question 6

Find the phase shift of the function.
-$$y = 4 \cos ( 3 \pi x + 2 )$$

Accepted Answer

A)  $\frac { 2 } { 3 \pi }$ units to the left 
B)  $\frac { 2 } { 3 }$ units to the right 
C)  2 units to the right 
D)  2 units to the left 
A)  $\frac { 2 } { 3 \pi }$ units to the left 
B)  $\frac { 2 } { 3 }$ units to the right 
C)  2 units to the right 
D)  2 units to the left

Question 7

Find the exact value of the indicated trigonometric function of $\theta$
-$\cos \theta = \frac { 2 } { 5 } , \quad \tan \theta < 0$
Find $\sin \theta$.

Accepted Answer

A)  $- \frac { 3 } { 2 }$ 
B)  $- \frac { \sqrt { 5 } } { 2 }$ 
C)  $- \sqrt { 5 }$ 
D)  $- \frac { \sqrt { 21 } } { 5 }$ 
A)  $- \frac { 3 } { 2 }$ 
B)  $- \frac { \sqrt { 5 } } { 2 }$ 
C)  $- \sqrt { 5 }$ 
D)  $- \frac { \sqrt { 21 } } { 5 }$

Question 8

Use transformations to graph the function.
-$$y = \cos \left( x + \frac { \pi } { 4 } \right)$$
 
 A)

Accepted Answer

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

Question 9

Solve the problem.
-$\sin \theta = \frac { 2 \sqrt { 2 } } { 3 } , \cos \theta = \frac { 1 } { 3 } \quad$ Find $\csc \theta .$

Accepted Answer

A)  $\frac { \sqrt { 15 } } { 15 }$ 
B)  $\frac { 3 \sqrt { 2 } } { 4 }$ 
C)  $\sqrt { 15 }$ 
D)  $\frac { 4 \sqrt { 15 } } { 15 }$ 
A)  $\frac { \sqrt { 15 } } { 15 }$ 
B)  $\frac { 3 \sqrt { 2 } } { 4 }$ 
C)  $\sqrt { 15 }$ 
D)  $\frac { 4 \sqrt { 15 } } { 15 }$

Question 10

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

Accepted Answer

A)  $1 ^ { \circ }$ 
B)  $- 36 ^ { \circ }$ 
C)  $- 1 ^ { \circ }$ 
D)  $- 36 \pi ^ { \circ }$ 
A)  $1 ^ { \circ }$ 
B)  $- 36 ^ { \circ }$ 
C)  $- 1 ^ { \circ }$ 
D)  $- 36 \pi ^ { \circ }$

Question 11

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
-$\mathrm { r } = 15.3$ centimeters, $\theta = 3.5$ radians, $\mathrm { s } =$ ?

Accepted Answer

A)  $55.6 \mathrm {~cm}$ 
B)  $53.6 \mathrm {~cm}$ 
C)  $52.6 \mathrm {~cm}$ 
D)  $54.6 \mathrm {~cm}$ 
A)  $55.6 \mathrm {~cm}$ 
B)  $53.6 \mathrm {~cm}$ 
C)  $52.6 \mathrm {~cm}$ 
D)  $54.6 \mathrm {~cm}$

Question 12

Solve the problem.
-For what numbers $x , 0 \leq x \leq 2 \pi$, does $\sin x = - 1$ ?

Accepted Answer

A)  $\pi$ 
B)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  none 
A)  $\pi$ 
B)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $\frac { 3 \pi } { 2 }$ 
D)  none

Question 13

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$$\csc \left( - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  0 
D)  undefined 
A)  1 
B)  $- 1$ 
C)  0 
D)  undefined

Question 14

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\tan \left( - \frac { \pi } { 3 } \right)$

Accepted Answer

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

Question 15

Find the exact value. Do not use a calculator.
-$\cos \frac { 3 \pi } { 2 }$

Accepted Answer

A)  1 
B)  -1 
C)  0 
D)  undefined 
A)  1 
B)  -1 
C)  0 
D)  undefined

Question 16

Solve the problem.
-The force acting on a pendulum to bring it to its perpendicular resting point is called the restoring force. The rest force $\mathrm { F }$, in Newtons, acting on a string pendulum is given by the formula
$$\mathrm { F } = \mathrm { mg } \sin \theta$$
where $\mathrm { m }$ is the mass in kilograms of the pendulum's bob, $g \approx 9.8$ meters per second per second is the acceleration due to gravity, and $\theta$ is angle at which the pendulum is displaced from the perpendicular. What is the value of the restoring force when $\mathrm { m } = 0.8$ kilogram and $\theta = 31 ^ { \circ }$ ? If necessary, round the answer to the nearest tenth of a Newton.

Accepted Answer

A)  3.2 N 
B)  3.8 N 
C)  6.7 N 
D)  4 N 
A)  3.2 N 
B)  3.8 N 
C)  6.7 N 
D)  4 N

Question 17

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\cos 3$

Accepted Answer

A)  -0.99 
B)  0.99 
C)  -1.00 
D)  1.00 
A)  -0.99 
B)  0.99 
C)  -1.00 
D)  1.00

Question 18

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.
-$\left( \frac { 4 } { 9 } , - \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find $\csc t$

Accepted Answer

A)  $\frac { \sqrt { 65 } } { 4 }$ 
B)  $\frac { \sqrt { 65 } } { 9 }$
$C ) - \frac { 9 \sqrt { 65 } } { 65 }$
$D ) = \frac { \sqrt { 65 } } { 9 }$ 
A)  $\frac { \sqrt { 65 } } { 4 }$ 
B)  $\frac { \sqrt { 65 } } { 9 }$
$C ) - \frac { 9 \sqrt { 65 } } { 65 }$
$D ) = \frac { \sqrt { 65 } } { 9 }$

Question 19

Solve the problem.
-For what numbers $x , 0 \leq x \leq 2 \pi$, does $\cos x = 1$ ?

Accepted Answer

A)  $0,2 \pi$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  none 
A)  $0,2 \pi$ 
B)  $\frac { \pi } { 2 }$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  none

Question 20

Find the exact value of the expression if θ = 60°. Do not use a calculator.
-$f ( \theta ) = \sin \theta \quad$ Find $f ( \theta )$.

Accepted Answer

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

Solve the problem. -If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 4$ , find the exact value of $f ( a ) + f ( a + \pi ) + f ( a + 3 \pi )$ .

Draw the angle. - $\frac { 2 \pi } { 3 }$

Find the area A. Round the answer to three decimal places. -

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - $r = 39.7$ centimeters, $\theta = \frac { \pi } { 14 }$ radians, $A =$ ?

Find the phase shift of the function. - $y = 4 \cos ( 3 \pi x + 2 )$

Find the exact value of the indicated trigonometric function of $\theta$ - $\cos \theta = \frac { 2 } { 5 } , \quad \tan \theta < 0$ Find $\sin \theta$ .

Solve the problem. - $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 } , \cos \theta = \frac { 1 } { 3 } \quad$ Find $\csc \theta .$

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

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = 15.3$ centimeters, $\theta = 3.5$ radians, $\mathrm { s } =$ ?

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\sin x = - 1$ ?

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - \frac { \pi } { 2 } \right)$

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\tan \left( - \frac { \pi } { 3 } \right)$

Find the exact value. Do not use a calculator. - $\cos \frac { 3 \pi } { 2 }$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cos 3$

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. - $\left( \frac { 4 } { 9 } , - \frac { \sqrt { 65 } } { 9 } \right) \quad$ Find $\csc t$

Solve the problem. -For what numbers $x , 0 \leq x \leq 2 \pi$ , does $\cos x = 1$ ?

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $f ( \theta ) = \sin \theta \quad$ Find $f ( \theta )$ .

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

Solve the problem. -If f(θ)=cot⁡θf ( \theta ) = \cot \thetaf(θ)=cotθ and f(a)=−4f ( a ) = - 4f(a)=−4 , find the exact value of f(a)+f(a+π)+f(a+3π)f ( a ) + f ( a + \pi ) + f ( a + 3 \pi )f(a)+f(a+π)+f(a+3π) .

Draw the angle. - 2π3\frac { 2 \pi } { 3 }32π​

Use transformations to graph the function. - y=5cos⁡(π−x)y=5 \cos (\pi-x)y=5cos(π−x) A) B) C) D)

Find the area A. Round the answer to three decimal places. -

If A denotes the area of the sector of a circle of radius r formed by the central angle θ, find the missing quantity. If necessary, round the answer to two decimal places. - r=39.7r = 39.7r=39.7 centimeters, θ=π14\theta = \frac { \pi } { 14 }θ=14π​ radians, A=A =A= ?

Find the phase shift of the function. - y=4cos⁡(3πx+2)y = 4 \cos ( 3 \pi x + 2 )y=4cos(3πx+2)

Find the exact value of the indicated trigonometric function of θ\thetaθ - cos⁡θ=25,tan⁡θ<0\cos \theta = \frac { 2 } { 5 } , \quad \tan \theta < 0cosθ=52​,tanθ<0 Find sin⁡θ\sin \thetasinθ .

Use transformations to graph the function. - y=cos⁡(x+π4)y = \cos \left( x + \frac { \pi } { 4 } \right)y=cos(x+4π​) A) B) C) D)

Solve the problem. - sin⁡θ=223,cos⁡θ=13\sin \theta = \frac { 2 \sqrt { 2 } } { 3 } , \cos \theta = \frac { 1 } { 3 } \quadsinθ=322​​,cosθ=31​ Find csc⁡θ.\csc \theta .cscθ.

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

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=15.3\mathrm { r } = 15.3r=15.3 centimeters, θ=3.5\theta = 3.5θ=3.5 radians, s=\mathrm { s } =s= ?

Solve the problem. -For what numbers x,0≤x≤2πx , 0 \leq x \leq 2 \pix,0≤x≤2π , does sin⁡x=−1\sin x = - 1sinx=−1 ?

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - csc⁡(−π2)\csc \left( - \frac { \pi } { 2 } \right)csc(−2π​)

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - tan⁡(−π3)\tan \left( - \frac { \pi } { 3 } \right)tan(−3π​)

Find the exact value. Do not use a calculator. - cos⁡3π2\cos \frac { 3 \pi } { 2 }cos23π​

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cos⁡3\cos 3cos3

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. - (49,−659)\left( \frac { 4 } { 9 } , - \frac { \sqrt { 65 } } { 9 } \right) \quad(94​,−965​​) Find csc⁡t\csc tcsct

Solve the problem. -For what numbers x,0≤x≤2πx , 0 \leq x \leq 2 \pix,0≤x≤2π , does cos⁡x=1\cos x = 1cosx=1 ?

Find the exact value of the expression if θ = 60°. Do not use a calculator. - f(θ)=sin⁡θf ( \theta ) = \sin \theta \quadf(θ)=sinθ Find f(θ)f ( \theta )f(θ) .