Question 1

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 2

Graph the function.
-$y=2 \tan (4 x)$

Accepted Answer

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

Question 3

Answer the question.
-Which one of the equations below matches the graph?

Accepted Answer

A)  $y = 4 \sin \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = 2 \cos \left( \frac { 1 } { 4 } x \right)$ 
D)  $y = 4 \cos ( 2 x )$ 
A)  $y = 4 \sin \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 4 \cos \left( \frac { 1 } { 2 } x \right)$ 
C)  $y = 2 \cos \left( \frac { 1 } { 4 } x \right)$ 
D)  $y = 4 \cos ( 2 x )$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places.

Accepted Answer

A)  $27.06$ in. 
B)  $28.8 \mathrm { in }$. 
C)  $31.31 \mathrm { in }$. 
D)  $30.03 \mathrm { in }$. 
A)  $27.06$ in. 
B)  $28.8 \mathrm { in }$. 
C)  $31.31 \mathrm { in }$. 
D)  $30.03 \mathrm { in }$.

Question 5

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

Accepted Answer

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

Question 6

Find an equation for the graph.
-

Accepted Answer

A)  $y = - 3 \sin ( 3 x )$ 
B)  $y = - 3 \cos ( 3 x )$ 
C)  $y = - 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
A)  $y = - 3 \sin ( 3 x )$ 
B)  $y = - 3 \cos ( 3 x )$ 
C)  $y = - 3 \cos \left( \frac { 1 } { 3 } x \right)$ 
D)  $y = 3 \cos \left( \frac { 1 } { 3 } x \right)$

Question 7

Graph the function.
-$$y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 8

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)  $\frac { \sqrt { 2 } } { 2 }$

Question 9

Name the quadrant in which the angle θ lies.
-$\tan \theta < 0 , \quad \sin \theta < 0$

Accepted Answer

A)  I 
B)  II 
C)  III 
D)  IV 
A)  I 
B)  II 
C)  III 
D)  IV

Question 10

Choose the one alternative that best completes the statement or answers the question.
Use transformations to graph the function.
-$$y = - 4 \sin \left( x + \frac { \pi } { 4 } \right)$$

Accepted Answer

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

Question 11

Match the function to its graph.
-$$y = - \tan x$$

Accepted Answer

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

Question 12

Choose the one alternative that best completes the statement or answers the question.
A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( 5,12 ) \quad$ Find $\sin \theta$.

Accepted Answer

A)  $- \frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $\frac { 5 } { 13 }$ 
A)  $- \frac { 12 } { 13 }$ 
B)  $- \frac { 5 } { 13 }$ 
C)  $\frac { 12 } { 13 }$ 
D)  $\frac { 5 } { 13 }$

Question 13

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

Accepted Answer

A)  0,1 
B)  $0 , \pi , 2 \pi$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  $0,1,2$ 
A)  0,1 
B)  $0 , \pi , 2 \pi$ 
C)  $\frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
D)  $0,1,2$

Question 14

Find the exact value of the indicated trigonometric function of θ.
-$\cos \theta = \frac { 2 } { 5 } , \quad \tan \theta < 0$
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 15

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
-Wildlife management personnel use predator-prey equations to model the populations of certain predators and
their prey in the wild. Suppose the population M of a predator after t months is given by $$M = 750 + 125 \sin \frac { \pi } { 6 } t$$ while the population N of its primary prey is given by $$N = 12,250 + 3050 \cos \frac { \pi } { 6 } t$$ Find the period for each of these functions.

Accepted Answer

The answer of Write the word or phrase that best...

Question 16

Graph the function. Show at least one period.
-$y=-3 \cos (x-\pi)$

Accepted Answer

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

Question 17

Find the exact value of the expression if θ = 45°. Do not use a calculator.
-$g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$.

Accepted Answer

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

Question 18

Solve the problem.
-A circle has a radius of 8 centimeters. Find the area of the sector of the circle formed by an angle of $60 ^ { \circ }$. If necessary, round the answer to two decimal places.

Accepted Answer

A)  $33.51 \mathrm {~cm} ^ { 2 }$ 
B)  $67.02 \mathrm {~cm} ^ { 2 }$ 
C)  $2.22 \mathrm {~cm} ^ { 2 }$ 
D)  $4.19 \mathrm {~cm} ^ { 2 }$ 
A)  $33.51 \mathrm {~cm} ^ { 2 }$ 
B)  $67.02 \mathrm {~cm} ^ { 2 }$ 
C)  $2.22 \mathrm {~cm} ^ { 2 }$ 
D)  $4.19 \mathrm {~cm} ^ { 2 }$

Question 19

Convert the angle to a decimal in degrees. Round the answer to two decimal places.
-127°58'55"

Accepted Answer

A)  $128.04 ^ { \circ }$ 
B)  $127.94 ^ { \circ }$ 
C)  $127.99 ^ { \circ }$ 
D)  $127.98 ^ { \circ }$ 
A)  $128.04 ^ { \circ }$ 
B)  $127.94 ^ { \circ }$ 
C)  $127.99 ^ { \circ }$ 
D)  $127.98 ^ { \circ }$

Question 20

Find the exact value of the expression if θ = 60°. Do not use a calculator.
-$f ( \theta ) = \sin \theta \quad$ Find $12 f ( \theta )$.

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $6 \sqrt { 3 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  6 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $6 \sqrt { 3 }$ 
C)  $- \frac { 1 } { 2 }$ 
D)  6

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

Graph the function. - $y=2 \tan (4 x)$ $Graph the function. - y=2 \tan (4 x)$

Answer the question. -Which one of the equations below matches the graph?

Choose the one alternative that best completes the statement or answers the question. -The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places.

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

Find an equation for the graph. -

Graph the function. - $y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$ $Graph the function. - y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$

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

Name the quadrant in which the angle θ lies. - $\tan \theta < 0 , \quad \sin \theta < 0$

Match the function to its graph. - $y = - \tan x$

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( 5,12 ) \quad$ Find $\sin \theta$ .

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

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

Graph the function. Show at least one period. - $y=-3 \cos (x-\pi)$ $Graph the function. Show at least one period. - y=-3 \cos (x-\pi)$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

Solve the problem. -A circle has a radius of 8 centimeters. Find the area of the sector of the circle formed by an angle of $60 ^ { \circ }$ . If necessary, round the answer to two decimal places.

Convert the angle to a decimal in degrees. Round the answer to two decimal places. -127°58'55"

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $f ( \theta ) = \sin \theta \quad$ Find $12 f ( \theta )$ .

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 5: Trigonometric Functions

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

Graph the function. - y=2tan⁡(4x)y=2 \tan (4 x)y=2tan(4x)

Answer the question. -Which one of the equations below matches the graph?

Choose the one alternative that best completes the statement or answers the question. -The minute hand of a clock is 5 inches long. How far does the tip of the minute hand move in 55 minutes? If necessary, round the answer to two decimal places.

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

Find an equation for the graph. -

Graph the function. - y=−2tan⁡(x−π4)y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)y=−2tan(x−4π​)

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) .

Name the quadrant in which the angle θ lies. - tan⁡θ<0,sin⁡θ<0\tan \theta < 0 , \quad \sin \theta < 0tanθ<0,sinθ<0

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=−4sin⁡(x+π4)y = - 4 \sin \left( x + \frac { \pi } { 4 } \right)y=−4sin(x+4π​)

Match the function to its graph. - y=−tan⁡xy = - \tan xy=−tanx

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (5,12)( 5,12 ) \quad(5,12) Find sin⁡θ\sin \thetasinθ .

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

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

Graph the function. Show at least one period. - y=−3cos⁡(x−π)y=-3 \cos (x-\pi)y=−3cos(x−π)

Find the exact value of the expression if θ = 45°. Do not use a calculator. - g(θ)=cos⁡θg ( \theta ) = \cos \theta \quadg(θ)=cosθ Find [g(θ)]2[ g ( \theta ) ] ^ { 2 }[g(θ)]2 .

Solve the problem. -A circle has a radius of 8 centimeters. Find the area of the sector of the circle formed by an angle of 60∘60 ^ { \circ }60∘ . If necessary, round the answer to two decimal places.

Convert the angle to a decimal in degrees. Round the answer to two decimal places. -127°58'55"

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 12f(θ)12 f ( \theta )12f(θ) .

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

Foundations: a Prelude to Functions

Graphing Utilities

Filters

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

Graph the function. - $y=2 \tan (4 x)$ $Graph the function. - y=2 \tan (4 x)$

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

Graph the function. - $y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$ $Graph the function. - y = - 2 \tan \left( x - \frac { \pi } { 4 } \right)$

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

Name the quadrant in which the angle θ lies. - $\tan \theta < 0 , \quad \sin \theta < 0$

Match the function to its graph. - $y = - \tan x$

Choose the one alternative that best completes the statement or answers the question. A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( 5,12 ) \quad$ Find $\sin \theta$ .

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

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

Graph the function. Show at least one period. - $y=-3 \cos (x-\pi)$ $Graph the function. Show at least one period. - y=-3 \cos (x-\pi)$

Find the exact value of the expression if θ = 45°. Do not use a calculator. - $g ( \theta ) = \cos \theta \quad$ Find $[ g ( \theta ) ] ^ { 2 }$ .

Solve the problem. -A circle has a radius of 8 centimeters. Find the area of the sector of the circle formed by an angle of $60 ^ { \circ }$ . If necessary, round the answer to two decimal places.

Find the exact value of the expression if θ = 60°. Do not use a calculator. - $f ( \theta ) = \sin \theta \quad$ Find $12 f ( \theta )$ .