Question 1

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\tan \theta = - \frac { \sqrt { 3 } } { 3 }$ and $\cos \theta > 0$

Accepted Answer

A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { 5 \pi } { 6 }$ 
C)  $\frac { 7 \pi } { 6 }$ 
D)  $\frac { 11 \pi } { 6 }$ 
A)  $\frac { 5 \pi } { 3 }$ 
B)  $\frac { 5 \pi } { 6 }$ 
C)  $\frac { 7 \pi } { 6 }$ 
D)  $\frac { 11 \pi } { 6 }$

Question 2

Describe the end behavior of the function.
-$$f ( x ) = 1.2 ^ { x } \sin 2 x$$

Accepted Answer

A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
C)  $\lim _ { x \rightarrow\infty  } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow\infty  } f ( x ) = 0$ 
A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = \infty$ 
C)  $\lim _ { x \rightarrow\infty  } f ( x ) = \infty$ 
D)  $\lim _ { x \rightarrow\infty  } f ( x ) = 0$

Question 3

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( - 2,5 ) ;$ find $\sin \theta$

Accepted Answer

A)  $- \frac { 5 } { 2 }$ 
B)  $\frac { 2 \sqrt { 29 } } { 29 }$ 
C)  $\frac { 5 \sqrt { 29 } } { 29 }$ 
D)  $\frac { \sqrt { 29 } } { 5 }$ 
A)  $- \frac { 5 } { 2 }$ 
B)  $\frac { 2 \sqrt { 29 } } { 29 }$ 
C)  $\frac { 5 \sqrt { 29 } } { 29 }$ 
D)  $\frac { \sqrt { 29 } } { 5 }$

Question 4

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\cot \theta = \frac { 5 } { 12 } ; \csc \theta$

Accepted Answer

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

Question 5

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$$\tan ^ { - 1 } ( - 0.7002 )$$

Accepted Answer

A)  $- 38 ^ { \circ }$ 
B)  $145 ^ { \circ }$ 
C)  $- 33 ^ { \circ }$ 
D)  $- 35 ^ { \circ }$ 
A)  $- 38 ^ { \circ }$ 
B)  $145 ^ { \circ }$ 
C)  $- 33 ^ { \circ }$ 
D)  $- 35 ^ { \circ }$

Question 6

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\sin \theta = \frac { 6 } { 7 } ; \cot \theta$

Accepted Answer

A)  $\frac { \sqrt { 13 } } { 7 }$ 
B)  $\frac { 6 } { \sqrt { 13 } }$ 
C)  $\frac { \sqrt { 13 } } { 6 }$ 
D)  $\frac { 7 } { \sqrt { 13 } }$ 
A)  $\frac { \sqrt { 13 } } { 7 }$ 
B)  $\frac { 6 } { \sqrt { 13 } }$ 
C)  $\frac { \sqrt { 13 } } { 6 }$ 
D)  $\frac { 7 } { \sqrt { 13 } }$

Question 7

Solve the equation.
-Solve $\cos \theta = 1$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$.

Accepted Answer

A)  $30 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $0 ^ { \circ }$ 
D)  $60 ^ { \circ }$ 
A)  $30 ^ { \circ }$ 
B)  $90 ^ { \circ }$ 
C)  $0 ^ { \circ }$ 
D)  $60 ^ { \circ }$

Question 8

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\sec \mathrm { A }$ and $\csc \mathrm { A }$.

Accepted Answer

A)  $\sec \mathrm { A } = \frac { 8 } { 17 } ; \csc \mathrm { A } = \frac { 15 } { 17 }$ 
B)  $\sec \mathrm { A } = \frac { 17 } { 8 } ; \csc \mathrm { A } = \frac { 17 } { 15 }$ 
C)  $\sec \mathrm { A } = \frac { 17 } { 15 } ; \csc \mathrm { A } = \frac { 17 } { 8 }$ 
D)  $\sec A = \frac { 15 } { 8 } ; \csc A = \frac { 8 } { 15 }$ 
A)  $\sec \mathrm { A } = \frac { 8 } { 17 } ; \csc \mathrm { A } = \frac { 15 } { 17 }$ 
B)  $\sec \mathrm { A } = \frac { 17 } { 8 } ; \csc \mathrm { A } = \frac { 17 } { 15 }$ 
C)  $\sec \mathrm { A } = \frac { 17 } { 15 } ; \csc \mathrm { A } = \frac { 17 } { 8 }$ 
D)  $\sec A = \frac { 15 } { 8 } ; \csc A = \frac { 8 } { 15 }$

Question 9

Choose the graph which matches the function.
-$$f ( x ) = \pi \sin 2 \pi x$$

Accepted Answer

A)  No damping 
B)  Damping factor $= 2 \pi$, damping occurs as $x \rightarrow 0$ 
C)  Damping factor $= \pi$, damping occurs as $\mathrm { x } \rightarrow \infty$ 
D)  Damping factor $= \pi$, damping occurs as $x \rightarrow 0$ 
A)  No damping 
B)  Damping factor $= 2 \pi$, damping occurs as $x \rightarrow 0$ 
C)  Damping factor $= \pi$, damping occurs as $\mathrm { x } \rightarrow \infty$ 
D)  Damping factor $= \pi$, damping occurs as $x \rightarrow 0$

Question 10

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
-$$y = - \tan \frac { 1 } { 9 } x + 7$$

Accepted Answer

A)  Reflection across the $x$-axis, horizontal shrink by a factor of $\frac { 1 } { 9 }$, and vertical translation down 7 units. 
B)  Horizontal stretch by a factor of 9 and a vertical translation up 7 units. 
C)  Reflection across the $x$-axis, horizontal translation to the right 9 units, and vertical translation up 7 units. 
D)  Reflection across the x-axis, horizontal stretch by a factor of 9 , and vertical translation up 7 units. 
A)  Reflection across the $x$-axis, horizontal shrink by a factor of $\frac { 1 } { 9 }$, and vertical translation down 7 units. 
B)  Horizontal stretch by a factor of 9 and a vertical translation up 7 units. 
C)  Reflection across the $x$-axis, horizontal translation to the right 9 units, and vertical translation up 7 units. 
D)  Reflection across the x-axis, horizontal stretch by a factor of 9 , and vertical translation up 7 units.

Question 11

Identify the maximum and minimum values of the function in the interval $ [-2 \pi, 2 \pi] $. Use your understanding of transformations, not your graphing calculator.
-$$y = - \frac { 1 } { 2 } \cos x$$

Accepted Answer

A)  Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= - \frac { 1 } { 2 }$ 
B)  Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= 0$ 
C)  Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= - \frac { 1 } { 4 }$ 
D)  Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= 0$ 
A)  Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= - \frac { 1 } { 2 }$ 
B)  Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= 0$ 
C)  Maximum value $= \frac { 1 } { 4 } ;$ minimum value $= - \frac { 1 } { 4 }$ 
D)  Maximum value $= \frac { 1 } { 2 } ;$ minimum value $= 0$

Question 12

Solve the problem.
-A 2600-lb car travelling uphill has a grade resistance of 120 pounds. Use a tangent function to estimate the angle of the grade. Give your answer to the nearest tenth.

Accepted Answer

A)  $5.3$ 
B)  $- 5.3$ 
C)  $- 2.6$ 
D)  $2.6$ 
A)  $5.3$ 
B)  $- 5.3$ 
C)  $- 2.6$ 
D)  $2.6$

Question 13

Solve the problem.
-From a boat on the lake, the angle of elevation to the top of a cliff is $33 ^ { \circ } 22 ^ { \prime }$. If the base of the cliff is 2101 feet from the boat, how high is the cliff (to the nearest foot)?

Accepted Answer

A)  $1384 \mathrm { ft }$ 
B)  $1397 \mathrm { ft }$ 
C)  $1387 \mathrm { ft }$ 
D)  $1394 \mathrm { ft }$ 
A)  $1384 \mathrm { ft }$ 
B)  $1397 \mathrm { ft }$ 
C)  $1387 \mathrm { ft }$ 
D)  $1394 \mathrm { ft }$

Question 14

Find the exact value of the composition.
-$\tan ^ { - 1 } \left( \tan \left( \frac { 3 \pi } { 4 } \right) \right)$

Accepted Answer

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

Question 15

Graph the function.
-$y=\sec 6 x$

Accepted Answer

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

Question 16

Find approximate solutions for the equation in the interval $ -\pi<\mathbf{X}<\pi $. Round to three decimal places.
-$\cot x = 2 \sec x$

Accepted Answer

A)  $1.571$ 
B)  $0.427,2.715$ 
C)  $- 1.571,1.571$ 
D)  $0.427$ 
A)  $1.571$ 
B)  $0.427,2.715$ 
C)  $- 1.571,1.571$ 
D)  $0.427$

Question 17

Find an algebraic expression equivalent to the given expression.
-$\sin \left( \tan ^ { - 1 } \frac { \mathrm { u } } { 2 } \right)$

Accepted Answer

A)  $\frac { \mathrm { u } } { 2 }$ 
B)  $\frac { u \sqrt { u ^ { 2 } + 4 } } { u ^ { 2 } + 4 }$ 
C)  $\frac { \sqrt { \mathrm { u } ^ { 2 } - 4 } } { \mathrm { u } }$ 
D)  $\frac { 2 } { \mathrm { u } }$ 
A)  $\frac { \mathrm { u } } { 2 }$ 
B)  $\frac { u \sqrt { u ^ { 2 } + 4 } } { u ^ { 2 } + 4 }$ 
C)  $\frac { \sqrt { \mathrm { u } ^ { 2 } - 4 } } { \mathrm { u } }$ 
D)  $\frac { 2 } { \mathrm { u } }$

Question 18

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-$\frac { \pi } { 4 }$

Accepted Answer

A)  $\frac { 9 \pi } { 4 } ; - \frac { \pi } { 4 }$ 
B)  $\frac { 5 \pi } { 4 } ; - \frac { 3 \pi } { 4 }$ 
C)  $\frac { \pi } { 4 } + 360 ^ { \circ } ; \frac { \pi } { 4 } - 360 ^ { \circ }$ 
D)  $\frac { 9 \pi } { 4 } ; - \frac { 7 \pi } { 4 }$ 
A)  $\frac { 9 \pi } { 4 } ; - \frac { \pi } { 4 }$ 
B)  $\frac { 5 \pi } { 4 } ; - \frac { 3 \pi } { 4 }$ 
C)  $\frac { \pi } { 4 } + 360 ^ { \circ } ; \frac { \pi } { 4 } - 360 ^ { \circ }$ 
D)  $\frac { 9 \pi } { 4 } ; - \frac { 7 \pi } { 4 }$

Question 19

Find the exact solution to the equation without a calculator.
-$$\sin ^ { - 1 } ( \sin x ) = \frac { \pi } { 6 }$$

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  $\pi$ 
C)  $\frac { \pi } { 12 }$ 
D)  0 
A)  $\frac { \pi } { 6 }$ 
B)  $\pi$ 
C)  $\frac { \pi } { 12 }$ 
D)  0

Question 20

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$$\tan \theta = \frac { 1 } { 3 } ; \csc \theta$$

Accepted Answer

A)  $\frac { 1 } { \sqrt { 10 } }$ 
B)  $\sqrt { 10 }$ 
C)  3 
D)  $\frac { \sqrt { 10 } } { 3 }$ 
A)  $\frac { 1 } { \sqrt { 10 } }$ 
B)  $\sqrt { 10 }$ 
C)  3 
D)  $\frac { \sqrt { 10 } } { 3 }$

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\tan \theta = - \frac { \sqrt { 3 } } { 3 }$ and $\cos \theta > 0$

Describe the end behavior of the function. - $f ( x ) = 1.2 ^ { x } \sin 2 x$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - 2,5 ) ;$ find $\sin \theta$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\cot \theta = \frac { 5 } { 12 } ; \csc \theta$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\tan ^ { - 1 } ( - 0.7002 )$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\sin \theta = \frac { 6 } { 7 } ; \cot \theta$

Solve the equation. -Solve $\cos \theta = 1$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$ .

Choose the graph which matches the function. - $f ( x ) = \pi \sin 2 \pi x$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. - $y = - \tan \frac { 1 } { 9 } x + 7$

Identify the maximum and minimum values of the function in the interval $[-2 \pi, 2 \pi]$ . Use your understanding of transformations, not your graphing calculator. - $y = - \frac { 1 } { 2 } \cos x$

Solve the problem. -A 2600-lb car travelling uphill has a grade resistance of 120 pounds. Use a tangent function to estimate the angle of the grade. Give your answer to the nearest tenth.

Solve the problem. -From a boat on the lake, the angle of elevation to the top of a cliff is $33 ^ { \circ } 22 ^ { \prime }$ . If the base of the cliff is 2101 feet from the boat, how high is the cliff (to the nearest foot)?

Find the exact value of the composition. - $\tan ^ { - 1 } \left( \tan \left( \frac { 3 \pi } { 4 } \right) \right)$

Graph the function. - $y=\sec 6 x$ $Graph the function. - y=\sec 6 x$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\cot x = 2 \sec x$

Find an algebraic expression equivalent to the given expression. - $\sin \left( \tan ^ { - 1 } \frac { \mathrm { u } } { 2 } \right)$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $\frac { \pi } { 4 }$

Find the exact solution to the equation without a calculator. - $\sin ^ { - 1 } ( \sin x ) = \frac { \pi } { 6 }$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\tan \theta = \frac { 1 } { 3 } ; \csc \theta$

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

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 4: Trigonometric Functions

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - tan⁡θ=−33\tan \theta = - \frac { \sqrt { 3 } } { 3 }tanθ=−33​​ and cos⁡θ>0\cos \theta > 0cosθ>0

Describe the end behavior of the function. - f(x)=1.2xsin⁡2xf ( x ) = 1.2 ^ { x } \sin 2 xf(x)=1.2xsin2x

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(−2,5);\mathrm { P } ( - 2,5 ) ;P(−2,5); find sin⁡θ\sin \thetasinθ

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - cot⁡θ=512;csc⁡θ\cot \theta = \frac { 5 } { 12 } ; \csc \thetacotθ=125​;cscθ

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - tan⁡−1(−0.7002)\tan ^ { - 1 } ( - 0.7002 )tan−1(−0.7002)

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - sin⁡θ=67;cot⁡θ\sin \theta = \frac { 6 } { 7 } ; \cot \thetasinθ=76​;cotθ

Solve the equation. -Solve cos⁡θ=1\cos \theta = 1cosθ=1 for θ\thetaθ , where 0∘≤θ≤90∘0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }0∘≤θ≤90∘ .

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find sec⁡A\sec \mathrm { A }secA and csc⁡A\csc \mathrm { A }cscA .

Choose the graph which matches the function. - f(x)=πsin⁡2πxf ( x ) = \pi \sin 2 \pi xf(x)=πsin2πx

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. - y=−tan⁡19x+7y = - \tan \frac { 1 } { 9 } x + 7y=−tan91​x+7

Identify the maximum and minimum values of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . Use your understanding of transformations, not your graphing calculator. - y=−12cos⁡xy = - \frac { 1 } { 2 } \cos xy=−21​cosx