Question 1

$$\text { Use properties of the graph of } f ( x ) = \cos x \text { to explain why } \cos \left( - 32 ^ { \circ } \right) = \cos 32 ^ { \circ } \text {. }$$

Accepted Answer

The cosine function is even an

Question 2

Solve the problem.
-A contractor needs to know the height of a building to estimate the cost of a job. From a point 90 feet away from the base of the building, the angle of elevation to the top of the building is found to be $41 ^ { \circ } 4 ^ { \prime }$. Find the height of the building. Round your answer to the hundredths place.

Accepted Answer

A)  $76.89 \mathrm { ft }$ 
B)  $81.32 \mathrm { ft }$ 
C)  $78.42 \mathrm { ft }$ 
D)  $82.65 \mathrm { ft }$ 
A)  $76.89 \mathrm { ft }$ 
B)  $81.32 \mathrm { ft }$ 
C)  $78.42 \mathrm { ft }$ 
D)  $82.65 \mathrm { ft }$

Question 3

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\cot 0.1596$

Accepted Answer

A)  $6.2124$ 
B)  $1.0129$ 
C)  $0.1610$ 
D)  $0.9873$ 
A)  $6.2124$ 
B)  $1.0129$ 
C)  $0.1610$ 
D)  $0.9873$

Question 4

Choose the graph which matches the function.
-$$y = \sin x + \cos 2 x - \sin 3 x - \cos 4 x$$

Accepted Answer

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

Question 5

Solve the problem.
-From a distance of 43 feet from the base of a building, the angle of elevation to the top of the building is 67°. Estimate the height of the building to the nearest foot.

Accepted Answer

A)  101 feet 
B)  40 feet 
C)  18 feet 
D)  17 feet 
A)  101 feet 
B)  40 feet 
C)  18 feet 
D)  17 feet

Question 6

Give the exact value.
-$\sec 30 ^ { \circ }$

Accepted Answer

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

Question 7

Solve the problem.
-A car wheel has a 13 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward $5 \mathrm { ft }$ ?

Accepted Answer

A)  $274.4 ^ { \circ }$ 
B)  $269.4 ^ { \circ }$ 
C)  $279.4 ^ { \circ }$ 
D)  $264.4 ^ { \circ }$ 
A)  $274.4 ^ { \circ }$ 
B)  $269.4 ^ { \circ }$ 
C)  $279.4 ^ { \circ }$ 
D)  $264.4 ^ { \circ }$

Question 8

Solve the problem.
-A rotating beacon is located $6 \mathrm { ft }$ from a wall. If the distance from the beacon to the point on the wall where the $b$ is aimed is given by
$$a = 6 | \sec 2 \pi t | \text {, }$$
where $t$ is in seconds, find a when $t = 0.28$ seconds. Round your answer to the nearest hundredth.

Accepted Answer

A)  $20.72 \mathrm { ft }$ 
B)  $- 32.02 \mathrm { ft }$ 
C)  $32.02 \mathrm { ft }$ 
D)  $9.41 \mathrm { ft }$ 
A)  $20.72 \mathrm { ft }$ 
B)  $- 32.02 \mathrm { ft }$ 
C)  $32.02 \mathrm { ft }$ 
D)  $9.41 \mathrm { ft }$

Question 9

Find the zeros of the function in the interval $ [-2 \pi, 2 \pi] $.
-$$f ( x ) = - 4 \sin 2 x$$

Accepted Answer

A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $0 , \pm \pi , \pm 2 \pi$ 
C)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$ 
D)  $0 , \pm \frac { \pi } { 2 } , \pm \pi , \pm \frac { 3 \pi } { 2 } , \pm 2 \pi$ 
A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $0 , \pm \pi , \pm 2 \pi$ 
C)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$ 
D)  $0 , \pm \frac { \pi } { 2 } , \pm \pi , \pm \frac { 3 \pi } { 2 } , \pm 2 \pi$

Question 10

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

Accepted Answer

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

Question 11

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\tan \theta = - 1$ and $\sin \theta > 0$

Accepted Answer

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

Question 12

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$$\sin \theta = \frac { 9 } { 10 } ; \cos \theta$$

Accepted Answer

A)  $\frac { 10 } { 9 }$ 
B)  $\frac { 10 } { \sqrt { 19 } }$ 
C)  $\frac { \sqrt { 19 } } { 10 }$ 
D)  $\frac { \sqrt { 19 } } { 9 }$ 
A)  $\frac { 10 } { 9 }$ 
B)  $\frac { 10 } { \sqrt { 19 } }$ 
C)  $\frac { \sqrt { 19 } } { 10 }$ 
D)  $\frac { \sqrt { 19 } } { 9 }$

Question 13

Evaluate without using a calculator by using ratios in a reference triangle.
-$\csc 60 ^ { \circ }$

Accepted Answer

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

Question 14

Find the domain and range of the function.
-$$f ( x ) = 3 x + \sin x$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $[ - 1,1 ]$ 
B)  Domain: $[ 0,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $[ - 1,1 ]$; range: $[ - 3,3 ]$ 
D)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
A)  Domain: $( - \infty , \infty )$; range: $[ - 1,1 ]$ 
B)  Domain: $[ 0,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $[ - 1,1 ]$; range: $[ - 3,3 ]$ 
D)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$

Question 15

Evaluate without using a calculator by using ratios in a reference triangle.
-$\tan \left( - \frac { 2 \pi } { 3 } \right)$

Accepted Answer

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

Question 16

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three
decimal places.
-$\csc ^ { - 1 } ( 1.8292 )$

Accepted Answer

A)  $- 3.720$ 
B)  $3.720$ 
C)  $0.578$ 
D)  $0.733$ 
A)  $- 3.720$ 
B)  $3.720$ 
C)  $0.578$ 
D)  $0.733$

Question 17

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point.
-Amplitude 6, period $\pi / 6$, point $( 1 / 4,0 )$

Accepted Answer

A)  $y = 6 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right)$ 
B)  $y = 6 \sin ( 12 x - 3 )$ 
C)  $y = 6 \sin \left( 12 x - \frac { \pi } { 4 } \right)$ 
D)  $y = 6 \sin \left( 6 x - \frac { 3 } { 2 } \right)$ 
A)  $y = 6 \sin \left( \frac { \pi } { 6 } x - \frac { \pi } { 4 } \right)$ 
B)  $y = 6 \sin ( 12 x - 3 )$ 
C)  $y = 6 \sin \left( 12 x - \frac { \pi } { 4 } \right)$ 
D)  $y = 6 \sin \left( 6 x - \frac { 3 } { 2 } \right)$

Question 18

Choose the point on the terminal side of .
-$$\theta = 60 ^ { \circ }$$

Accepted Answer

A)  $( - \sqrt { 3 } , 1 )$ 
B)  $( 1 , \sqrt { 3 } )$ 
C)  $( - 1 , \sqrt { 3 } )$ 
D)  $( - \sqrt { 3 } , - 1 )$ 
A)  $( - \sqrt { 3 } , 1 )$ 
B)  $( 1 , \sqrt { 3 } )$ 
C)  $( - 1 , \sqrt { 3 } )$ 
D)  $( - \sqrt { 3 } , - 1 )$

Question 19

Solve the equation.
-Solve $\tan \theta = \sqrt { 3 }$ for $\theta$, where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$.

Accepted Answer

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

Question 20

Evaluate without using a calculator.
-$\sin \alpha$, if $\cot \alpha = 8$ and $\sec \alpha < 0$

Accepted Answer

A)  $- \sqrt { 65 }$ 
B)  $- \frac { 8 \sqrt { 65 } } { 65 }$ 
C)  $- \frac { \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 65 } } { 65 }$ 
A)  $- \sqrt { 65 }$ 
B)  $- \frac { 8 \sqrt { 65 } } { 65 }$ 
C)  $- \frac { \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 65 } } { 65 }$

$\text { Use properties of the graph of } f ( x ) = \cos x \text { to explain why } \cos \left( - 32 ^ { \circ } \right) = \cos 32 ^ { \circ } \text {. }$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\cot 0.1596$

Choose the graph which matches the function. - $y = \sin x + \cos 2 x - \sin 3 x - \cos 4 x$

Solve the problem. -From a distance of 43 feet from the base of a building, the angle of elevation to the top of the building is 67°. Estimate the height of the building to the nearest foot.

Give the exact value. - $\sec 30 ^ { \circ }$

Solve the problem. -A car wheel has a 13 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward $5 \mathrm { ft }$ ?

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = - 4 \sin 2 x$

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

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\tan \theta = - 1$ and $\sin \theta > 0$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\sin \theta = \frac { 9 } { 10 } ; \cos \theta$

Evaluate without using a calculator by using ratios in a reference triangle. - $\csc 60 ^ { \circ }$

Find the domain and range of the function. - $f ( x ) = 3 x + \sin x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\tan \left( - \frac { 2 \pi } { 3 } \right)$

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - $\csc ^ { - 1 } ( 1.8292 )$

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 6, period $\pi / 6$ , point $( 1 / 4,0 )$

Choose the point on the terminal side of . - $\theta = 60 ^ { \circ }$

Solve the equation. -Solve $\tan \theta = \sqrt { 3 }$ for $\theta$ , where $0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$ .

Evaluate without using a calculator. - $\sin \alpha$ , if $\cot \alpha = 8$ and $\sec \alpha < 0$

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

Prerequisites

Filters

Exam 4: Trigonometric Functions

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - cot⁡0.1596\cot 0.1596cot0.1596

Choose the graph which matches the function. - y=sin⁡x+cos⁡2x−sin⁡3x−cos⁡4xy = \sin x + \cos 2 x - \sin 3 x - \cos 4 xy=sinx+cos2x−sin3x−cos4x

Solve the problem. -From a distance of 43 feet from the base of a building, the angle of elevation to the top of the building is 67°. Estimate the height of the building to the nearest foot.

Give the exact value. - sec⁡30∘\sec 30 ^ { \circ }sec30∘

Solve the problem. -A car wheel has a 13 -inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward 5ft5 \mathrm { ft }5ft ?

Find the zeros of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . - f(x)=−4sin⁡2xf ( x ) = - 4 \sin 2 xf(x)=−4sin2x

Use a calculator to graph the function. - y=xcos⁡xy = x \cos xy=xcosx

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - tan⁡θ=−1\tan \theta = - 1tanθ=−1 and sin⁡θ>0\sin \theta > 0sinθ>0

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - sin⁡θ=910;cos⁡θ\sin \theta = \frac { 9 } { 10 } ; \cos \thetasinθ=109​;cosθ

Evaluate without using a calculator by using ratios in a reference triangle. - csc⁡60∘\csc 60 ^ { \circ }csc60∘

Find the domain and range of the function. - f(x)=3x+sin⁡xf ( x ) = 3 x + \sin xf(x)=3x+sinx

Evaluate without using a calculator by using ratios in a reference triangle. - tan⁡(−2π3)\tan \left( - \frac { 2 \pi } { 3 } \right)tan(−32π​)

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - csc⁡−1(1.8292)\csc ^ { - 1 } ( 1.8292 )csc−1(1.8292)

Write an equation for a sine curve that has the given amplitude and period, and which passes through the given point. -Amplitude 6, period π/6\pi / 6π/6 , point (1/4,0)( 1 / 4,0 )(1/4,0)

Choose the point on the terminal side of . - θ=60∘\theta = 60 ^ { \circ }θ=60∘

Solve the equation. -Solve tan⁡θ=3\tan \theta = \sqrt { 3 }tanθ=3​ for θ\thetaθ , where 0∘≤θ≤90∘0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }0∘≤θ≤90∘ .

Evaluate without using a calculator. - sin⁡α\sin \alphasinα , if cot⁡α=8\cot \alpha = 8cotα=8 and sec⁡α<0\sec \alpha < 0secα<0