Question 1

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

Accepted Answer

A)  $y = 5 \sin ( x - 3 )$ 
B)  $y = \sin ( 5 x + 3 )$ 
C)  $y = 5 \sin ( 2 x + 6 )$ 
D)  $y = 5 \sin \left( \frac { 1 } { 2 } x - 6 \right)$ 
A)  $y = 5 \sin ( x - 3 )$ 
B)  $y = \sin ( 5 x + 3 )$ 
C)  $y = 5 \sin ( 2 x + 6 )$ 
D)  $y = 5 \sin \left( \frac { 1 } { 2 } x - 6 \right)$

Question 2

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

Accepted Answer

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

Question 3

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity.
-$\mathrm { s } = 4.84$ meters, $\theta = 2.2$ radians, $\mathrm { r } =$ ?

Accepted Answer

A)  $1.1 \mathrm {~m}$ 
B)  $2.2 \mathrm {~m}$ 
C)  $1.5 \mathrm {~m}$ 
D)  $0.45 \mathrm {~m}$ 
A)  $1.1 \mathrm {~m}$ 
B)  $2.2 \mathrm {~m}$ 
C)  $1.5 \mathrm {~m}$ 
D)  $0.45 \mathrm {~m}$

Question 4

Find an equation for the graph.
-

Accepted Answer

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

Question 5

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)  $\frac { 2 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$

Question 6

Solve the problem.
-Which of the following trigonometric values are negative? I. $\quad \sin \left( - 292 ^ { \circ } \right)$
II. $\tan \left( - 193 ^ { \circ } \right)$
III. $\cos \left( - 207 ^ { \circ } \right)$
IV. $\cot 222 ^ { \circ }$

Accepted Answer

A)  II, III, and IV 
B)  I and III 
C)  III only 
D)  II and III 
A)  II, III, and IV 
B)  I and III 
C)  III only 
D)  II and III

Question 7

Convert the angle to a decimal in degrees. Round the answer to two decimal places.
-$21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }$

Accepted Answer

A)  $21.22 ^ { \circ }$ 
B)  $21.29 ^ { \circ }$ 
C)  $21.34 ^ { \circ }$ 
D)  $21.37 ^ { \circ }$ 
A)  $21.22 ^ { \circ }$ 
B)  $21.29 ^ { \circ }$ 
C)  $21.34 ^ { \circ }$ 
D)  $21.37 ^ { \circ }$

Question 8

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

Accepted Answer

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

Question 9

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 10

Graph the sinusoidal function.
-$y=4 \cos (\pi x)$

Accepted Answer

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

Question 11

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 12

Find the exact value. Do not use a calculator.
-$\tan 45 ^ { \circ }$

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\cot 390 ^ { \circ }$

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
-A boy is flying a model airplane while standing on a straight line. The plane, at the end of a twenty-five foot wire, flies in circles around the boy. The directed distance of the plane from the straight line is found to be
$$d = 25 \cos \left( \frac { 3 \pi } { 4 } t \right)$$ where d is measured in feet and t is the time in seconds. If d > 0, the plane is in front of the boy; if d < 0, the plane is
behind him.
What is the amplitude? What is the period?
Graph d over two periods beginning at t = 0.

Accepted Answer

None

Question 16

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

Accepted Answer

A)  $\frac { 4 - \sqrt { 2 } } { 2 }$ 
B)  $\frac { 4 - \sqrt { 3 } } { 2 }$ 
C)  $\frac { 4 \sqrt { 2 } - 3 \sqrt { 3 } } { 6 }$ 
D)  $\frac { 4 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$ 
A)  $\frac { 4 - \sqrt { 2 } } { 2 }$ 
B)  $\frac { 4 - \sqrt { 3 } } { 2 }$ 
C)  $\frac { 4 \sqrt { 2 } - 3 \sqrt { 3 } } { 6 }$ 
D)  $\frac { 4 \sqrt { 3 } - 3 \sqrt { 2 } } { 6 }$

Question 17

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 18

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places.
-$\sqrt { 7 }$

Accepted Answer

A)  $0.05 ^ { \circ }$ 
B)  $151.59 ^ { \circ }$ 
C)  $151.47 ^ { \circ }$ 
D)  $- 0.04 ^ { \circ }$ 
A)  $0.05 ^ { \circ }$ 
B)  $151.59 ^ { \circ }$ 
C)  $151.47 ^ { \circ }$ 
D)  $- 0.04 ^ { \circ }$

Question 19

Solve the problem.
-For what numbers $x , - 2 \pi \leq x \leq 2 \pi$, does the graph of $y = \csc x$ have vertical asymptotes?

Accepted Answer

A)  $- 2 , - 1,0,1,2$ 
B)  $- \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $- 2 \pi , - \pi , 0 , \pi , 2 \pi$ 
D)  none 
A)  $- 2 , - 1,0,1,2$ 
B)  $- \frac { 3 \pi } { 2 } , - \frac { \pi } { 2 } , \frac { \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $- 2 \pi , - \pi , 0 , \pi , 2 \pi$ 
D)  none

Question 20

Write the word or phrase that best completes each statement or answers the question.
-$\sin \theta = \frac { 1 } { 6 } , \quad \sec \theta < 0$
Find $\cos \theta$ and $\tan \theta$.

Accepted Answer

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

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

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

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - $\mathrm { s } = 4.84$ meters, $\theta = 2.2$ radians, $\mathrm { r } =$ ?

Find an equation for the graph. -

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

Solve the problem. -Which of the following trigonometric values are negative? I. $\quad \sin \left( - 292 ^ { \circ } \right)$ II. $\tan \left( - 193 ^ { \circ } \right)$ III. $\cos \left( - 207 ^ { \circ } \right)$ IV. $\cot 222 ^ { \circ }$

Convert the angle to a decimal in degrees. Round the answer to two decimal places. - $21 ^ { \circ } 17 ^ { \prime } 34 ^ { \prime \prime }$

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

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 $\csc t$

Graph the sinusoidal function. - $y=4 \cos (\pi x)$ $Graph the sinusoidal function. - y=4 \cos (\pi x)$

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. Do not use a calculator. - $\tan 45 ^ { \circ }$

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

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\cot 390 ^ { \circ }$

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

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

Convert the angle in radians to degrees. Express the answer in decimal form, rounded to two decimal places. - $\sqrt { 7 }$

Solve the problem. -For what numbers $x , - 2 \pi \leq x \leq 2 \pi$ , does the graph of $y = \csc x$ have vertical asymptotes?

Write the word or phrase that best completes each statement or answers the question. - $\sin \theta = \frac { 1 } { 6 } , \quad \sec \theta < 0$ Find $\cos \theta$ and $\tan \theta$ .

Functions and Their Graphs

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Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

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Exam 5: Trigonometric Functions

Write the equation of a sine function that has the given characteristics. -Amplitude: 5 Period: π\piπ Phase Shift: - 3

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

If s denotes the length of the arc of a circle of radius r subtended by a central angle θ, find the missing quantity. - s=4.84\mathrm { s } = 4.84s=4.84 meters, θ=2.2\theta = 2.2θ=2.2 radians, r=\mathrm { r } =r= ?