Question 1

Find the exact value of the indicated trigonometric function of $\theta$
-$\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

Accepted Answer

A)  $- \frac { 3 \sqrt { 13 } } { 13 }$ 
B)  $- \frac { \sqrt { 13 } } { 3 }$ 
C)  $\frac { 3 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 2 }$ 
A)  $- \frac { 3 \sqrt { 13 } } { 13 }$ 
B)  $- \frac { \sqrt { 13 } } { 3 }$ 
C)  $\frac { 3 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 2 }$

Question 2

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

Accepted Answer

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

Question 3

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

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 4

Graph the function.
-$y=-\cot (2 x)$
 
 A)

Accepted Answer

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

Question 5

Solve the problem.
-The number of hours of sunlight in a day can be modeled by a sinusoidal function. In the northern hemisphere, the longest day of the year occurs at the summer solstice and the shortest day occurs at the winter solstice. In 2000, these
Dates were June 22 (the 172nd day of the year) and December 21 (the 356th day of the year), respectively. A town experiences $11.23$ hours of sunlight at the summer solstice and $8.03$ hours of sunlight at the winter solstice. Find a sinusoidal function $y = A \sin ( \omega x - \varphi ) + B$ that fits the data, where $x$ is the day of the year. (Note: There are 366 days in the year 2000.)

Accepted Answer

A)  $y = 1.6 \sin \left( \frac { \pi } { 183 } x - \frac { 161 \pi } { 366 } \right) + 9.63$ 
B)  $y = 11.23 \sin \left( \frac { 172 \pi } { 356 } x - \frac { 2 \pi } { 3 } \right) + 9.63$ 
C)  $y = 1.6 \sin \left( \frac { \pi } { 183 } x - \frac { 2 \pi } { 3 } \right) + 9.63$ 
D)  $y = 11.23 \sin \left( \pi x - \frac { 2 \pi } { 3 } \right) + 8.03$ 
A)  $y = 1.6 \sin \left( \frac { \pi } { 183 } x - \frac { 161 \pi } { 366 } \right) + 9.63$ 
B)  $y = 11.23 \sin \left( \frac { 172 \pi } { 356 } x - \frac { 2 \pi } { 3 } \right) + 9.63$ 
C)  $y = 1.6 \sin \left( \frac { \pi } { 183 } x - \frac { 2 \pi } { 3 } \right) + 9.63$ 
D)  $y = 11.23 \sin \left( \pi x - \frac { 2 \pi } { 3 } \right) + 8.03$

Question 6

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

Accepted Answer

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

Question 7

Solve the problem.
-An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of $\frac { 1 } { 5 }$ radian is swept out, what is the linear speed of the object?

Accepted Answer

A)  $\frac { 1 } { 4 } \mathrm {~m} / \mathrm { sec }$ 
B)  $\frac { 1 } { 8 } \mathrm {~m} / \mathrm { sec }$ 
C)  $\frac { 2 } { 5 } \mathrm {~m} / \mathrm { sec }$ 
D)  $\frac { 1 } { 5 } \mathrm {~m} / \mathrm { sec }$ 
A)  $\frac { 1 } { 4 } \mathrm {~m} / \mathrm { sec }$ 
B)  $\frac { 1 } { 8 } \mathrm {~m} / \mathrm { sec }$ 
C)  $\frac { 2 } { 5 } \mathrm {~m} / \mathrm { sec }$ 
D)  $\frac { 1 } { 5 } \mathrm {~m} / \mathrm { sec }$

Question 8

Graph the function.
-$$y = 4 \tan \left( \frac { 1 } { 2 } x \right)$$
 
 A)

Accepted Answer

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

Question 9

Without graphing the function, determine its amplitude or period as requested.
-$y = 5 \sin \frac { 1 } { 4 } x \quad$ Find the amplitude.

Accepted Answer

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

Question 10

Use transformations to graph the function.
-$y=5 \sin x+1$

Accepted Answer

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

Question 11

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)  $- \frac { 1 } { 2 }$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Find the exact value. 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 15

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ.
-$( - 2 , - 1 ) \quad$ Find $\csc \theta .$

Accepted Answer

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

Question 16

Solve the problem.
-The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is 12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does the wiper cover in one cycle?
(Round to the nearest 0.1 square inch.) A) $1041.8$ in $^ { 2 }$

Accepted Answer

B)  $1105.3 \mathrm { in } ^ { 2 }$ 
C)  $948.3 \mathrm { in } ^ { 2 }$ 
D)  $1036.7$ in $^ { 2 }$ 
B)  $1105.3 \mathrm { in } ^ { 2 }$ 
C)  $948.3 \mathrm { in } ^ { 2 }$ 
D)  $1036.7$ in $^ { 2 }$

Question 17

Write the equation of a sine function that has the given characteristics.
-Amplitude: 3
Period: $5 \pi$
Phase Shift: $- \frac { \pi } { 5 }$

Accepted Answer

A)  $y = 3 \sin \left( \frac { 2 } { 5 } x + \frac { 2 } { 25 } \pi \right)$ 
B)  $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { 2 } { 25 } \pi \right)$ 
C)  $y = 3 \sin \left( \frac { 5 } { 2 } x - \frac { 2 } { 25 } \pi \right)$ 
D)  $y = 3 \sin \left( 6 x - \frac { \pi } { 6 } \right)$ 
A)  $y = 3 \sin \left( \frac { 2 } { 5 } x + \frac { 2 } { 25 } \pi \right)$ 
B)  $y = 3 \sin \left( \frac { 2 } { 5 } x - \frac { 2 } { 25 } \pi \right)$ 
C)  $y = 3 \sin \left( \frac { 5 } { 2 } x - \frac { 2 } { 25 } \pi \right)$ 
D)  $y = 3 \sin \left( 6 x - \frac { \pi } { 6 } \right)$

Question 18

Find the exact value of the indicated trigonometric function of $\theta$
-$\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$.

Accepted Answer

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

Question 19

Graph the sinusoidal function.
-$$y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)$$
 
 A)

Accepted Answer

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

Question 20

Find the exact value of the expression. Do not use a calculator.
-$\cot 45 ^ { \circ } - \sin 60 ^ { \circ }$

Accepted Answer

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

Find the exact value of the indicated trigonometric function of $\theta$ - $\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

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

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

Graph the function. - $y=-\cot (2 x)$ $Graph the function. - y=-\cot (2 x) A) B) C) D)$ A) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ B) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ C) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ D) $Graph the function. - y=-\cot (2 x) A) B) C) D)$

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

Solve the problem. -An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of $\frac { 1 } { 5 }$ radian is swept out, what is the linear speed of the object?

Without graphing the function, determine its amplitude or period as requested. - $y = 5 \sin \frac { 1 } { 4 } x \quad$ Find the amplitude.

Use transformations to graph the function. - $y=5 \sin x+1$ $Use transformations to graph the function. - y=5 \sin x+1$

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

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

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

Find the exact value. Do not use a calculator. - $\csc \left( - \frac { \pi } { 2 } \right)$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 2 , - 1 ) \quad$ Find $\csc \theta .$

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $5 \pi$ Phase Shift: $- \frac { \pi } { 5 }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$ .

Find the exact value of the expression. Do not use a calculator. - $\cot 45 ^ { \circ } - \sin 60 ^ { \circ }$

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 indicated trigonometric function of θ\thetaθ - tan⁡θ=−89,θ\tan \theta = - \frac { 8 } { 9 } , \quad \thetatanθ=−98​,θ in quadrant II \quad Find cos⁡θ\cos \thetacosθ

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

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

Graph the function. - y=−cot⁡(2x)y=-\cot (2 x)y=−cot(2x) A) B) C) D)

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 ?

Solve the problem. -An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of 15\frac { 1 } { 5 }51​ radian is swept out, what is the linear speed of the object?

Graph the function. - y=4tan⁡(12x)y = 4 \tan \left( \frac { 1 } { 2 } x \right)y=4tan(21​x) A) B) C) D)

Without graphing the function, determine its amplitude or period as requested. - y=5sin⁡14xy = 5 \sin \frac { 1 } { 4 } x \quady=5sin41​x Find the amplitude.

Use transformations to graph the function. - y=5sin⁡x+1y=5 \sin x+1y=5sinx+1

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) .

Solve the problem. -If f(θ)=cos⁡θf ( \theta ) = \cos \thetaf(θ)=cosθ and f(a)=−14f ( a ) = - \frac { 1 } { 4 }f(a)=−41​ , find the exact value of f(−a)f ( - a )f(−a) .

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

Find the exact value. Do not use a calculator. - csc⁡(−π2)\csc \left( - \frac { \pi } { 2 } \right)csc(−2π​)

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - (−2,−1)( - 2 , - 1 ) \quad(−2,−1) Find csc⁡θ.\csc \theta .cscθ.

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: 5π5 \pi5π Phase Shift: −π5- \frac { \pi } { 5 }−5π​

Find the exact value of the indicated trigonometric function of θ\thetaθ - csc⁡θ=−94,θ\csc \theta = - \frac { 9 } { 4 } , \quad \thetacscθ=−49​,θ in quadrant III \quad Find cot⁡θ\cot \thetacotθ .

Graph the sinusoidal function. - y=73cos⁡(−12x)y = \frac { 7 } { 3 } \cos \left( - \frac { 1 } { 2 } x \right)y=37​cos(−21​x) A) B) C) D)

Find the exact value of the expression. Do not use a calculator. - cot⁡45∘−sin⁡60∘\cot 45 ^ { \circ } - \sin 60 ^ { \circ }cot45∘−sin60∘

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 indicated trigonometric function of $\theta$ - $\tan \theta = - \frac { 8 } { 9 } , \quad \theta$ in quadrant II $\quad$ Find $\cos \theta$

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

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

Graph the function. - $y=-\cot (2 x)$ $Graph the function. - y=-\cot (2 x) A) B) C) D)$ A) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ B) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ C) $Graph the function. - y=-\cot (2 x) A) B) C) D)$ D) $Graph the function. - y=-\cot (2 x) A) B) C) D)$

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

Solve the problem. -An object is traveling around a circle with a radius of 20 meters. If in 10 seconds a central angle of $\frac { 1 } { 5 }$ radian is swept out, what is the linear speed of the object?

Without graphing the function, determine its amplitude or period as requested. - $y = 5 \sin \frac { 1 } { 4 } x \quad$ Find the amplitude.

Use transformations to graph the function. - $y=5 \sin x+1$ $Use transformations to graph the function. - y=5 \sin x+1$

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

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

Find the exact value. Do not use a calculator. - $\csc \left( - \frac { \pi } { 2 } \right)$

A point on the terminal side of an angle θ is given. Find the exact value of the indicated trigonometric function of θ. - $( - 2 , - 1 ) \quad$ Find $\csc \theta .$

Write the equation of a sine function that has the given characteristics. -Amplitude: 3 Period: $5 \pi$ Phase Shift: $- \frac { \pi } { 5 }$

Find the exact value of the indicated trigonometric function of $\theta$ - $\csc \theta = - \frac { 9 } { 4 } , \quad \theta$ in quadrant III $\quad$ Find $\cot \theta$ .

Find the exact value of the expression. Do not use a calculator. - $\cot 45 ^ { \circ } - \sin 60 ^ { \circ }$