Question 1

Solve for x in the given interval.
-$\cot x = - 1 , \frac { \pi } { 2 } \leq x \leq \pi$

Accepted Answer

A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 6 }$ 
D)  $\frac { 2 \pi } { 3 }$ 
A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { 5 \pi } { 6 }$ 
D)  $\frac { 2 \pi } { 3 }$

Question 2

Solve the problem.
-A boat sails for 5 hours at $20 \mathrm { mph }$ in a direction $173.52 ^ { \circ }$. How far south has it sailed (to the nearest mile)?

Accepted Answer

A)  $97 \mathrm { mi }$ 
B)  $95 \mathrm { mi }$ 
C)  $101 \mathrm { mi }$ 
D)  $99 \mathrm { mi }$ 
A)  $97 \mathrm { mi }$ 
B)  $95 \mathrm { mi }$ 
C)  $101 \mathrm { mi }$ 
D)  $99 \mathrm { mi }$

Question 3

Use a calculator to solve for x in the given interval
-$\cos \theta = 0.4801,0 \leq \theta \leq \frac { \pi } { 2 }$

Accepted Answer

A)  $0.50$ 
B)  $5.21$ 
C)  $1.07$ 
D)  $0.89$ 
A)  $0.50$ 
B)  $5.21$ 
C)  $1.07$ 
D)  $0.89$

Question 4

Use a calculator to graph the function.
-$y=\sin x-x$

Accepted Answer

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

Question 5

Find the zeros of the function in the interval $ [-2 \pi, 2 \pi] $.
-$$f ( x ) = 5 \cos \frac { x } { 2 }$$

Accepted Answer

A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$ 
C)  $\pm \pi$ 
D)  $\pm \pi , \pm 2 \pi$ 
A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$ 
C)  $\pm \pi$ 
D)  $\pm \pi , \pm 2 \pi$

Question 6

Find the exact value of the composition.
-$$\sin \left( 2 \arccos \left( \frac { 3 } { 5 } \right) \right)$$

Accepted Answer

A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 14 } { 25 }$ 
C)  $\frac { 24 } { 25 }$ 
D)  $\frac { 7 } { 25 }$ 
A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 14 } { 25 }$ 
C)  $\frac { 24 } { 25 }$ 
D)  $\frac { 7 } { 25 }$

Question 7

Solve the problem.
-Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius 7 units, with linear speed 5 units per second.

Accepted Answer

A)  $x = 7 \cos 5 t , y = 7 \sin 5 t$ 
B)  $x = 5 \cos 7 t , y = 7 \sin 5 t$ 
C)  $x = \cos 7 t + 5 , y = \sin 7 t + 5$ 
D)  $x = 7 \sin 5 t , y = 7 \sin 5 t$ 
A)  $x = 7 \cos 5 t , y = 7 \sin 5 t$ 
B)  $x = 5 \cos 7 t , y = 7 \sin 5 t$ 
C)  $x = \cos 7 t + 5 , y = \sin 7 t + 5$ 
D)  $x = 7 \sin 5 t , y = 7 \sin 5 t$

Question 8

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\sin 0.2525$

Accepted Answer

A)  $1.033$ 
B)  $0.2498$ 
C)  $0.9683$ 
D)  $0.2580$ 
A)  $1.033$ 
B)  $0.2498$ 
C)  $0.9683$ 
D)  $0.2580$

Question 9

Graph the function.
-$y=-1.5 \sin x$

Accepted Answer

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

Question 10

Solve the problem.
-At an altitude of $3500 \mathrm { ft }$, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 4 miles away by land? (Round your answer to the nearest tenth of a degree.)

Accepted Answer

A)  $10.4 ^ { \circ }$ 
B)  $9.4 ^ { \circ }$ 
C)  $89.9 ^ { \circ }$ 
D)  $88.9 ^ { \circ }$ 
A)  $10.4 ^ { \circ }$ 
B)  $9.4 ^ { \circ }$ 
C)  $89.9 ^ { \circ }$ 
D)  $88.9 ^ { \circ }$

Question 11

Find the trigonometric function value for the angle shown.
-$\sin \theta$

Accepted Answer

A)  $\sin \theta = - \frac { 2 \sqrt { 34 } } { 17 }$ 
B)  $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$ 
C)  $\sin \theta = - \frac { 4 \sqrt { 34 } } { 34 }$ 
D)  $\sin \theta = \frac { 3 \sqrt { 2 } } { 4 }$ 
A)  $\sin \theta = - \frac { 2 \sqrt { 34 } } { 17 }$ 
B)  $\sin \theta = \frac { 2 \sqrt { 2 } } { 3 }$ 
C)  $\sin \theta = - \frac { 4 \sqrt { 34 } } { 34 }$ 
D)  $\sin \theta = \frac { 3 \sqrt { 2 } } { 4 }$

Question 12

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\sin \mathrm { B }$ and $\tan \mathrm { B }$.

Accepted Answer

A)  $\sin \mathrm { B } = \frac { 7 } { 24 } ; \tan \mathrm { B } = \frac { 7 } { 25 }$ 
B)  $\sin B = \frac { 25 } { 7 } ; \tan B = \frac { 24 } { 7 }$ 
C)  $\sin B = \frac { 24 } { 25 } ; \tan B = \frac { 24 } { 7 }$ 
D)  $\sin B = \frac { 7 } { 25 } ; \tan B = \frac { 7 } { 24 }$ 
A)  $\sin \mathrm { B } = \frac { 7 } { 24 } ; \tan \mathrm { B } = \frac { 7 } { 25 }$ 
B)  $\sin B = \frac { 25 } { 7 } ; \tan B = \frac { 24 } { 7 }$ 
C)  $\sin B = \frac { 24 } { 25 } ; \tan B = \frac { 24 } { 7 }$ 
D)  $\sin B = \frac { 7 } { 25 } ; \tan B = \frac { 7 } { 24 }$

Question 13

Solve the equation.
-Solve $\csc \theta = 2$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Accepted Answer

A)  $30 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $30 ^ { \circ }$ 
B)  $45 ^ { \circ }$ 
C)  $90 ^ { \circ }$ 
D)  $60 ^ { \circ }$

Question 14

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$P ( - 15,36 )$; find $\sin \theta$.

Accepted Answer

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

Question 15

Find the exact value of the real number y.
-$$y = \csc ^ { - 1 } ( - 1 )$$

Accepted Answer

A)  $- \frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $2 \pi$ 
D)  $\pi$ 
A)  $- \frac { \pi } { 2 }$ 
B)  $\frac { \pi } { 4 }$ 
C)  $2 \pi$ 
D)  $\pi$

Question 16

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x).
-$$f ( x ) = \sin \left( x - \frac { \pi } { 2 } \right) ; g ( x ) = \sin \left( x + \frac { \pi } { 3 } \right)$$

Accepted Answer

A)  Translate to the left $\frac { 5 \pi } { 6 }$ units 
B)  Translate to the right $\frac { 5 \pi } { 6 }$ units 
C)  Translate to the right $\frac { \pi } { 6 }$ units 
D)  Translate to the left $\frac { \pi } { 2 }$ units 
A)  Translate to the left $\frac { 5 \pi } { 6 }$ units 
B)  Translate to the right $\frac { 5 \pi } { 6 }$ units 
C)  Translate to the right $\frac { \pi } { 6 }$ units 
D)  Translate to the left $\frac { \pi } { 2 }$ units

Question 17

Write the word or phrase that best completes each statement or answers the question.
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior.
-f(x) = - 2 cot x

Accepted Answer

Domain: All reals except integer multipl

Question 18

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\cos \theta = - \frac { \sqrt { 2 } } { 2 }$ and $\tan \theta > 0$

Accepted Answer

A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { 4 \pi } { 3 }$ 
D)  $\frac { \pi } { 4 }$ 
A)  $\frac { 5 \pi } { 4 }$ 
B)  $\frac { 3 \pi } { 4 }$ 
C)  $\frac { 4 \pi } { 3 }$ 
D)  $\frac { \pi } { 4 }$

Question 19

Solve the right triangle for all missing sides and angles to the nearest tenth.
-

Accepted Answer

A)  $20.89$ 
B)  $24.89$ 
C)  $10.28$ 
D)  $12.26$ 
A)  $20.89$ 
B)  $24.89$ 
C)  $10.28$ 
D)  $12.26$

Question 20

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( 5 , - 8 )$; find $\cos \theta$.

Accepted Answer

A)  $\frac { 5 \sqrt { 89 } } { 89 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 8 \sqrt { 89 } } { 89 }$ 
D)  $\frac { \sqrt { 89 } } { 5 }$ 
A)  $\frac { 5 \sqrt { 89 } } { 89 }$ 
B)  $- \frac { 5 } { 8 }$ 
C)  $\frac { 8 \sqrt { 89 } } { 89 }$ 
D)  $\frac { \sqrt { 89 } } { 5 }$

Solve for x in the given interval. - $\cot x = - 1 , \frac { \pi } { 2 } \leq x \leq \pi$

Solve the problem. -A boat sails for 5 hours at $20 \mathrm { mph }$ in a direction $173.52 ^ { \circ }$ . How far south has it sailed (to the nearest mile)?

Use a calculator to solve for x in the given interval - $\cos \theta = 0.4801,0 \leq \theta \leq \frac { \pi } { 2 }$

Use a calculator to graph the function. - $y=\sin x-x$ $Use a calculator to graph the function. - y=\sin x-x$

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = 5 \cos \frac { x } { 2 }$

Find the exact value of the composition. - $\sin \left( 2 \arccos \left( \frac { 3 } { 5 } \right) \right)$

Solve the problem. -Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius 7 units, with linear speed 5 units per second.

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\sin 0.2525$

Graph the function. - $y=-1.5 \sin x$ $Graph the function. - y=-1.5 \sin x$

Solve the problem. -At an altitude of $3500 \mathrm { ft }$ , the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 4 miles away by land? (Round your answer to the nearest tenth of a degree.)

Find the trigonometric function value for the angle shown. - $\sin \theta$ $Find the trigonometric function value for the angle shown. - \sin \theta$

Solve the equation. -Solve $\csc \theta = 2$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $P ( - 15,36 )$ ; find $\sin \theta$ .

Find the exact value of the real number y. - $y = \csc ^ { - 1 } ( - 1 )$

Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). - $f ( x ) = \sin \left( x - \frac { \pi } { 2 } \right) ; g ( x ) = \sin \left( x + \frac { \pi } { 3 } \right)$

Write the word or phrase that best completes each statement or answers the question. Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = - 2 cot x

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\cos \theta = - \frac { \sqrt { 2 } } { 2 }$ and $\tan \theta > 0$

Solve the right triangle for all missing sides and angles to the nearest tenth. -

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 5 , - 8 )$ ; find $\cos \theta$ .

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

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Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 4: Trigonometric Functions

Solve for x in the given interval. - cot⁡x=−1,π2≤x≤π\cot x = - 1 , \frac { \pi } { 2 } \leq x \leq \picotx=−1,2π​≤x≤π

Solve the problem. -A boat sails for 5 hours at 20mph20 \mathrm { mph }20mph in a direction 173.52∘173.52 ^ { \circ }173.52∘ . How far south has it sailed (to the nearest mile)?

Use a calculator to solve for x in the given interval - cos⁡θ=0.4801,0≤θ≤π2\cos \theta = 0.4801,0 \leq \theta \leq \frac { \pi } { 2 }cosθ=0.4801,0≤θ≤2π​

Use a calculator to graph the function. - y=sin⁡x−xy=\sin x-xy=sinx−x

Find the zeros of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . - f(x)=5cos⁡x2f ( x ) = 5 \cos \frac { x } { 2 }f(x)=5cos2x​

Find the exact value of the composition. - sin⁡(2arccos⁡(35))\sin \left( 2 \arccos \left( \frac { 3 } { 5 } \right) \right)sin(2arccos(53​))