Question 1

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$g ( \theta ) = \sin \theta \quad$ Find $12 g ( \theta )$.

Accepted Answer

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

Question 2

Solve the problem.
-A ship in the Atlantic Ocean measures its position to be 30°48' north latitude. Another ship is reported to be due north of the first ship at 41°17' north latitude. Approximately how far apart are the two ships? Round to the
Nearest mile. Assume that the radius of the Earth is 3960 miles.

Accepted Answer

A)  725 mi 
B)  75,966 mi 
C)  75,991 mi 
D)  1,351 mi 
A)  725 mi 
B)  75,966 mi 
C)  75,991 mi 
D)  1,351 mi A

Question 3

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\sin 67 ^ { \circ }$

Accepted Answer

A)  $0.92$ 
B)  $1.03$ 
C)  $- 0.75$ 
D)  $- 0.86$ 
A)  $0.92$ 
B)  $1.03$ 
C)  $- 0.75$ 
D)  $- 0.86$ A

Question 4

Graph the function.
-$y=2 \sec (3 x)$

Accepted Answer

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

Question 5

Choose the one alternative that best completes the statement or answers the question.
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 6

Find the exact value of the expression. Do not use a calculator.
-$$\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$$

Accepted Answer

A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 2 }$ 
D)  $\frac { 2 \sqrt { 2 } + 1 } { 6 }$ 
A)  0 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 2 } + 1 } { 2 }$ 
D)  $\frac { 2 \sqrt { 2 } + 1 } { 6 }$

Question 7

Solve the problem.
-What is the y-intercept of y = cos x?

Accepted Answer

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

Question 8

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

Accepted Answer

A)  $9.5 \mathrm { in }$. 
B)  $9.2$ in. 
C)  $9.3 \mathrm { in. }$ 
D)  $9.4 \mathrm { in }$. 
A)  $9.5 \mathrm { in }$. 
B)  $9.2$ in. 
C)  $9.3 \mathrm { in. }$ 
D)  $9.4 \mathrm { in }$.

Question 9

Find an equation for the graph.
-

Accepted Answer

A)  $y = 3 \cos \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 3 \cos ( 2 x )$ 
C)  $y = 2 \cos ( 3 x )$ 
D)  $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$ 
A)  $y = 3 \cos \left( \frac { 1 } { 2 } x \right)$ 
B)  $y = 3 \cos ( 2 x )$ 
C)  $y = 2 \cos ( 3 x )$ 
D)  $y = 5 \cos \left( \frac { 1 } { 2 } x \right)$

Question 10

Find an equation for the graph.
-

Accepted Answer

A)  $y = 4 \cos \left( \frac { \pi } { 3 } x \right)$ 
B)  $y = 3 \cos \left( \frac { \pi } { 5 } x \right)$ 
C)  $y = 3 \cos ( 5 \pi x )$ 
D)  $y = 5 \cos ( 3 \pi x )$ 
A)  $y = 4 \cos \left( \frac { \pi } { 3 } x \right)$ 
B)  $y = 3 \cos \left( \frac { \pi } { 5 } x \right)$ 
C)  $y = 3 \cos ( 5 \pi x )$ 
D)  $y = 5 \cos ( 3 \pi x )$

Question 11

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\sin 495 ^ { \circ }$

Accepted Answer

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

Question 12

Match the given function to its graph.
-1) $y = \sin \left( \frac { 1 } { 3 } x \right)$
2) $y = \frac { 1 } { 3 } \cos x$
3) $y = \frac { 1 } { 3 } \sin x$
4) $y = \cos \left( \frac { 1 } { 3 } x \right)$

Accepted Answer

A)

1A, 2D, 3C, 4B 
B) 
 
1B, 2D, 3C, 4A 
C)

1A, 2C, 3D, 4B 
D) 
 
 1A, 2B, 3C, 4D 
A)

1A, 2D, 3C, 4B 
B) 
 
1B, 2D, 3C, 4A 
C)

1A, 2C, 3D, 4B 
D) 
 
 1A, 2B, 3C, 4D

Question 13

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\cot \frac { \pi } { 8 }$

Accepted Answer

A)  1.26 
B)  91.30 
C)  1.38 
D)  91.18 
A)  1.26 
B)  91.30 
C)  1.38 
D)  91.18

Question 14

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 15

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.
-$$\mathrm { r } = 22.1 \text { feet, } \theta = 11.19 ^ { \circ } , \mathrm { A } = \text { ? }$$

Accepted Answer

A)  $50.69 \mathrm { ft } ^ { 2 }$ 
B)  $98.38 \mathrm { ft } ^ { 2 }$ 
C)  $95.38 \mathrm { ft } ^ { 2 }$ 
D)  $47.69 \mathrm { ft } ^ { 2 }$ 
A)  $50.69 \mathrm { ft } ^ { 2 }$ 
B)  $98.38 \mathrm { ft } ^ { 2 }$ 
C)  $95.38 \mathrm { ft } ^ { 2 }$ 
D)  $47.69 \mathrm { ft } ^ { 2 }$

Question 16

Solve the problem.
-If $\sin \theta = 0.9$, find $\sin ( \theta + \pi )$.

Accepted Answer

A)  $0.1$ 
B)  $- 0.1$ 
C)  $0.9$ 
D)  $- 0.9$ 
A)  $0.1$ 
B)  $- 0.1$ 
C)  $0.9$ 
D)  $- 0.9$

Question 17

Match the function to its graph.
-$$y = - \tan \left( x + \frac { \pi } { 2 } \right)$$

Accepted Answer

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

Question 18

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\tan 37 ^ { \circ }$

Accepted Answer

A)  0.60 
B)  0.75 
C)  0.80 
D)  -0.84 
A)  0.60 
B)  0.75 
C)  0.80 
D)  -0.84

Question 19

Name the quadrant in which the angle θ lies.
-$\csc \theta > 0 , \quad \sec \theta > 0$

Accepted Answer

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

Question 20

Find the exact value. Do not use a calculator.
-$\sec \frac { 13 \pi } { 4 }$

Accepted Answer

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

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $12 g ( \theta )$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sin 67 ^ { \circ }$

Graph the function. - $y=2 \sec (3 x)$ $Graph the function. - y=2 \sec (3 x)$

Choose the one alternative that best completes the statement or answers the question. 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. Do not use a calculator. - $\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$

Solve the problem. -What is the y-intercept of y = cos x?

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

Find an equation for the graph. -

Find an equation for the graph. -

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\sin 495 ^ { \circ }$

Match the given function to its graph. -1) $y = \sin \left( \frac { 1 } { 3 } x \right)$ 2) $y = \frac { 1 } { 3 } \cos x$ 3) $y = \frac { 1 } { 3 } \sin x$ 4) $y = \cos \left( \frac { 1 } { 3 } x \right)$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cot \frac { \pi } { 8 }$

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

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. - $\mathrm { r } = 22.1 \text { feet, } \theta = 11.19 ^ { \circ } , \mathrm { A } = \text { ? }$

Solve the problem. -If $\sin \theta = 0.9$ , find $\sin ( \theta + \pi )$ .

Match the function to its graph. - $y = - \tan \left( x + \frac { \pi } { 2 } \right)$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 37 ^ { \circ }$

Name the quadrant in which the angle θ lies. - $\csc \theta > 0 , \quad \sec \theta > 0$

Find the exact value. Do not use a calculator. - $\sec \frac { 13 \pi } { 4 }$

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

Find the exact value of the expression if θ = 30°. Do not use a calculator. - g(θ)=sin⁡θg ( \theta ) = \sin \theta \quadg(θ)=sinθ Find 12g(θ)12 g ( \theta )12g(θ) .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - sin⁡67∘\sin 67 ^ { \circ }sin67∘

Graph the function. - y=2sec⁡(3x)y=2 \sec (3 x)y=2sec(3x)

Choose the one alternative that best completes the statement or answers the question. 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​)

Find the exact value of the expression. Do not use a calculator. - tan⁡7π4+tan⁡5π4\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }tan47π​+tan45π​

Solve the problem. -What is the y-intercept of y = cos x?

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\mathrm { r } = 8.8r=8.8 inches, θ=60∘,s=\theta = 60 ^ { \circ } , \mathrm { s } =θ=60∘,s= ?

Find an equation for the graph. -

Find an equation for the graph. -

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - sin⁡495∘\sin 495 ^ { \circ }sin495∘

Match the given function to its graph. -1) y=sin⁡(13x)y = \sin \left( \frac { 1 } { 3 } x \right)y=sin(31​x) 2) y=13cos⁡xy = \frac { 1 } { 3 } \cos xy=31​cosx 3) y=13sin⁡xy = \frac { 1 } { 3 } \sin xy=31​sinx 4) y=cos⁡(13x)y = \cos \left( \frac { 1 } { 3 } x \right)y=cos(31​x)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cot⁡π8\cot \frac { \pi } { 8 }cot8π​

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​

Solve the problem. -If sin⁡θ=0.9\sin \theta = 0.9sinθ=0.9 , find sin⁡(θ+π)\sin ( \theta + \pi )sin(θ+π) .

Match the function to its graph. - y=−tan⁡(x+π2)y = - \tan \left( x + \frac { \pi } { 2 } \right)y=−tan(x+2π​)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - tan⁡37∘\tan 37 ^ { \circ }tan37∘

Name the quadrant in which the angle θ lies. - csc⁡θ>0,sec⁡θ>0\csc \theta > 0 , \quad \sec \theta > 0cscθ>0,secθ>0

Find the exact value. Do not use a calculator. - sec⁡13π4\sec \frac { 13 \pi } { 4 }sec413π​

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

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $g ( \theta ) = \sin \theta \quad$ Find $12 g ( \theta )$ .

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\sin 67 ^ { \circ }$

Graph the function. - $y=2 \sec (3 x)$ $Graph the function. - y=2 \sec (3 x)$

Choose the one alternative that best completes the statement or answers the question. 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. Do not use a calculator. - $\tan \frac { 7 \pi } { 4 } + \tan \frac { 5 \pi } { 4 }$

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { r } = 8.8$ 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. - $\sin 495 ^ { \circ }$

Match the given function to its graph. -1) $y = \sin \left( \frac { 1 } { 3 } x \right)$ 2) $y = \frac { 1 } { 3 } \cos x$ 3) $y = \frac { 1 } { 3 } \sin x$ 4) $y = \cos \left( \frac { 1 } { 3 } x \right)$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cot \frac { \pi } { 8 }$

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

Solve the problem. -If $\sin \theta = 0.9$ , find $\sin ( \theta + \pi )$ .

Match the function to its graph. - $y = - \tan \left( x + \frac { \pi } { 2 } \right)$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\tan 37 ^ { \circ }$

Name the quadrant in which the angle θ lies. - $\csc \theta > 0 , \quad \sec \theta > 0$

Find the exact value. Do not use a calculator. - $\sec \frac { 13 \pi } { 4 }$