Question 1

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\csc 660 ^ { \circ }$

Accepted Answer

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

Question 2

Draw the angle.
-135° A)

Accepted Answer

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

Question 3

Solve the problem.
-As part of an experiment to test different liquid fertilizers, a sprinkler has to be set to cover an area of 120 square yards in the shape of a sector of a circle of radius 30 yards. Through what angle should the sprinkler be
Set to rotate? If necessary, round the answer to two decimal places.

Accepted Answer

A)  48° 
B)  7.64° 
C)  15.28° 
D)  11.46° 
A)  48° 
B)  7.64° 
C)  15.28° 
D)  11.46°

Question 4

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

Accepted Answer

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

Question 5

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°. If necessary, round the answer to two decimal places. A) $33.51 \mathrm {~cm} ^ { 2 }$

Accepted Answer

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

Question 6

Solve the problem.
-For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30°. Round to the nearest hundredth.

Accepted Answer

A)  6.28 ft 
B)  4.19 ft 
C)  376.99 ft 
D)  2.09 ft 
A)  6.28 ft 
B)  4.19 ft 
C)  376.99 ft 
D)  2.09 ft

Question 7

Solve the problem.
-To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 11 revolutions per minute, what is the speed of the current? If
Necessary, round to two decimal places.

Accepted Answer

A)  0.06 mph 
B)  34.56 mph 
C)  0.2 mph 
D)  0.39 mph 
A)  0.06 mph 
B)  34.56 mph 
C)  0.2 mph 
D)  0.39 mph

Question 8

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

Question 9

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

Accepted Answer

A)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$ 
B)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm { D } , 4 \mathrm {~B}$ 
C)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm {~B} , 4 \mathrm { D }$ 
D)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm {~A} , 4 \mathrm { C }$ 
A)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm { D } , 4 \mathrm {~B}$ 
B)  $1 \mathrm { C } , 2 \mathrm {~A} , 3 \mathrm { D } , 4 \mathrm {~B}$ 
C)  $1 \mathrm {~A} , 2 \mathrm { C } , 3 \mathrm {~B} , 4 \mathrm { D }$ 
D)  $1 \mathrm {~B} , 2 \mathrm { D } , 3 \mathrm {~A} , 4 \mathrm { C }$

Question 10

Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\cos \left( - 60 ^ { \circ } \right)$

Accepted Answer

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

Question 11

Find the exact value of the expression. Do not use a calculator.
-$\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

Accepted Answer

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

Question 12

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\cos \frac { 16 \pi } { 3 }$

Accepted Answer

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

Question 13

Solve the problem.
-If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$, find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$

Accepted Answer

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

Question 14

Solve the problem.
-An experiment in a wind tunnel generates cyclic waves. The following data is collected for 52 seconds: $$\begin{array} { c | c } 
\begin{array} { c } 
\text { Time } \
\text { (in seconds)(in feet per second }
\end{array} & \begin{array} { c } 
\text { Wind speed } \
\text { fin }
\end{array} \
\hline 0 & 16 \
\hline 13 & 38 \
\hline 26 & 60 \
\hline 39 & 38 \
\hline 52 & 16
\end{array}$$ Let V represent the wind speed (velocity) in feet per second and let t represent the time in seconds. Write a sine equation that describes the wave. A) $V = 22 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 38$

Accepted Answer

B)  $V = 44 \sin ( 52 t - 26 ) + 22$ 
C)  $V = 60 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 16$ 
D)  $V = 60 \sin ( 52 t - 26 ) + 16$ 
B)  $V = 44 \sin ( 52 t - 26 ) + 22$ 
C)  $V = 60 \sin \left( \frac { \pi } { 26 } t - \frac { \pi } { 2 } \right) + 16$ 
D)  $V = 60 \sin ( 52 t - 26 ) + 16$

Question 15

Solve the problem.
-What is the $y$-intercept of $y = \sec x$ ?

Accepted Answer

A)  0 
B)  1 
C)  $\frac { \pi } { 2 }$ 
D)  none 
A)  0 
B)  1 
C)  $\frac { \pi } { 2 }$ 
D)  none

Question 16

Find an equation for the graph.
-  A) $y = 3 \sin \left( \frac { 1 } { 5 } x \right)$

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

Graph the sinusoidal function.
-$$y = - 4 \sin \left( \frac { 1 } { 4 } x \right)$$
 
 A)

Accepted Answer

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

Question 19

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\csc 2 ^ { \circ }$

Accepted Answer

A)  28.65 
B)  1.05 
C)  28.70 
D)  1.10 
A)  28.65 
B)  1.05 
C)  28.70 
D)  1.10

Question 20

Solve the problem.
-If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 6$, find the exact value of $f ( - a )$.

Accepted Answer

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 660 ^ { \circ }$

Draw the angle. -135° A) B) C) D)

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30°. Round to the nearest hundredth.

Solve the problem. -To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 11 revolutions per minute, what is the speed of the current? If Necessary, round 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 $12 f ( \theta )$ .

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\cos \left( - 60 ^ { \circ } \right)$

Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\cos \frac { 16 \pi } { 3 }$

Solve the problem. -If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$ , find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$

Solve the problem. -What is the $y$ -intercept of $y = \sec x$ ?

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

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\csc 2 ^ { \circ }$

Solve the problem. -If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 6$ , find the exact value of $f ( - a )$ .

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - csc⁡660∘\csc 660 ^ { \circ }csc660∘

Draw the angle. -135° A) B) C) D)

Graph the function. - y=sec⁡(x−π6)y=\sec \left(x-\frac{\pi}{6}\right)y=sec(x−6π​) A) B) C) D)

Solve the problem. -For a circle of radius 4 feet, find the arc length s subtended by a central angle of 30°. Round to the nearest hundredth.

Solve the problem. -To approximate the speed of a river, a circular paddle wheel with radius 0.5 feet is lowered into the water. If the current causes the wheel to rotate at a speed of 11 revolutions per minute, what is the speed of the current? If Necessary, round to two decimal places.

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) .

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - cos⁡(−60∘)\cos \left( - 60 ^ { \circ } \right)cos(−60∘)

Find the exact value of the expression. Do not use a calculator. - cos⁡60∘+tan⁡60∘\cos 60 ^ { \circ } + \tan 60 ^ { \circ }cos60∘+tan60∘

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - cos⁡16π3\cos \frac { 16 \pi } { 3 }cos316π​

Solve the problem. -If f(θ)=sin⁡θf ( \theta ) = \sin \thetaf(θ)=sinθ and f(a)=−16f ( a ) = - \frac { 1 } { 6 }f(a)=−61​ , find the exact value of f(a)+f(a+2π)+f(a+4π)f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )f(a)+f(a+2π)+f(a+4π)

Solve the problem. -What is the yyy -intercept of y=sec⁡xy = \sec xy=secx ?

Find an equation for the graph. - A) y=3sin⁡(15x)y = 3 \sin \left( \frac { 1 } { 5 } x \right)y=3sin(51​x) B) y=3sin⁡(5x)y = 3 \sin ( 5 x )y=3sin(5x) C) y=5sin⁡(3x)y = 5 \sin ( 3 x )y=5sin(3x) D) y=5sin⁡(13x)y = 5 \sin \left( \frac { 1 } { 3 } x \right)y=5sin(31​x)

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

Graph the sinusoidal function. - y=−4sin⁡(14x)y = - 4 \sin \left( \frac { 1 } { 4 } x \right)y=−4sin(41​x) A) B) C) D)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - csc⁡2∘\csc 2 ^ { \circ }csc2∘

Solve the problem. -If f(θ)=cot⁡θf ( \theta ) = \cot \thetaf(θ)=cotθ and f(a)=−6f ( a ) = - 6f(a)=−6 , find the exact value of f(−a)f ( - a )f(−a) .

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\csc 660 ^ { \circ }$

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

Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\cos \left( - 60 ^ { \circ } \right)$

Find the exact value of the expression. Do not use a calculator. - $\cos 60 ^ { \circ } + \tan 60 ^ { \circ }$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\cos \frac { 16 \pi } { 3 }$

Solve the problem. -If $f ( \theta ) = \sin \theta$ and $f ( a ) = - \frac { 1 } { 6 }$ , find the exact value of $f ( a ) + f ( a + 2 \pi ) + f ( a + 4 \pi )$

Solve the problem. -What is the $y$ -intercept of $y = \sec x$ ?

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

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\csc 2 ^ { \circ }$

Solve the problem. -If $f ( \theta ) = \cot \theta$ and $f ( a ) = - 6$ , find the exact value of $f ( - a )$ .