Exam 4: Trigonometric Functions

Solve the problem. -The sprocket assembly on a bicycle consists of a chain and two sprockets, one on the pedal and the other on the rear wheel. If the sprocket on the pedal is 3 inches in diameter, the sprocket on the rear wheel is 2 inches in diameter, and the rear wheel is 26 inches in diameter, how fast is the bicycle traveling in miles per hour when the cyclist is pedaling at the rate of $0.6$ revolutions per second? Round your answer to the nearest tenth mph.

(Multiple Choice)

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Question 161

Find the specified quantity. -Find the phase shift of $y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)$

(Multiple Choice)

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Question 162

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

(Multiple Choice)

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Question 163

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, $\tan t$

(Multiple Choice)

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Question 164

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. - $y = 6 \cos x$

(Multiple Choice)

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Question 165

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = - 3 \tan ^ { - 1 } x$

(Essay)

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Question 166

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

(Multiple Choice)

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Question 167

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = 5 \cos x + 2 \sin x$

(Multiple Choice)

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Question 168

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

(Multiple Choice)

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Question 169

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 15,20 )$ ; find $\csc \theta$ .

(Multiple Choice)

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Question 170

Solve the equation. -Solve $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ , where $0 \leq \theta \leq \frac { \pi } { 2 }$ .

(Multiple Choice)

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Question 171

Solve for x in the given interval. - $\cot x = 1 , - 2 \pi \leq x \leq - \frac { 3 \pi } { 2 }$

(Multiple Choice)

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Question 172

Choose the graph which matches the function. - $f ( x ) = - 3 x ^ { 2 } \cos 5 x$

(Multiple Choice)

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Question 173

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 18 \sin \pi x - 16 \cos \pi x$

(True/False)

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Question 174

Evaluate without using a calculator by using ratios in a reference triangle. - $\sin \frac { 5 \pi } { 3 }$

(Multiple Choice)

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Question 175

Find the angle in degrees that describes the compass bearing. - $\mathrm { SE }$

(Multiple Choice)

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Question 176

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( 0.68 )$

(Multiple Choice)

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Question 177

Choose the graph which matches the function. - $f ( x ) = 3 ^ { - x } \cos 4 x$

(Multiple Choice)

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Question 178

Solve the problem. -The radius of a car wheel is 13 inches. How many revolutions per minute is the wheel making when the car is travelling at $45 \mathrm { mph }$ . Round your answer to the nearest revolution.

(Multiple Choice)

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Question 179

Give the exact value. - $\csc 60 ^ { \circ }$

(Multiple Choice)

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Question 180

Find the specified quantity. -Find the phase shift of $y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)$

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

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, $\tan t$

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. - $y = 6 \cos x$

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = - 3 \tan ^ { - 1 } x$

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

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = 5 \cos x + 2 \sin x$

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

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 15,20 )$ ; find $\csc \theta$ .

Solve the equation. -Solve $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ , where $0 \leq \theta \leq \frac { \pi } { 2 }$ .

Solve for x in the given interval. - $\cot x = 1 , - 2 \pi \leq x \leq - \frac { 3 \pi } { 2 }$

Choose the graph which matches the function. - $f ( x ) = - 3 x ^ { 2 } \cos 5 x$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 18 \sin \pi x - 16 \cos \pi x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\sin \frac { 5 \pi } { 3 }$

Find the angle in degrees that describes the compass bearing. - $\mathrm { SE }$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( 0.68 )$

Choose the graph which matches the function. - $f ( x ) = 3 ^ { - x } \cos 4 x$

Solve the problem. -The radius of a car wheel is 13 inches. How many revolutions per minute is the wheel making when the car is travelling at $45 \mathrm { mph }$ . Round your answer to the nearest revolution.

Give the exact value. - $\csc 60 ^ { \circ }$

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

Find the specified quantity. -Find the phase shift of y=4−2sin⁡(3x+π2)y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)y=4−2sin(3x+2π​)

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

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, tan⁡t\tan ttant

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=6cos⁡xy = 6 \cos xy=6cosx

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - f(x)=−3tan⁡−1xf ( x ) = - 3 \tan ^ { - 1 } xf(x)=−3tan−1x

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

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - f(x)=5cos⁡x+2sin⁡xf ( x ) = 5 \cos x + 2 \sin xf(x)=5cosx+2sinx

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

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(15,20)\mathrm { P } ( 15,20 )P(15,20) ; find csc⁡θ\csc \thetacscθ .

Solve the equation. -Solve sin⁡θ=32\sin \theta = \frac { \sqrt { 3 } } { 2 }sinθ=23​​ for θ\thetaθ , where 0≤θ≤π20 \leq \theta \leq \frac { \pi } { 2 }0≤θ≤2π​ .

Solve for x in the given interval. - cot⁡x=1,−2π≤x≤−3π2\cot x = 1 , - 2 \pi \leq x \leq - \frac { 3 \pi } { 2 }cotx=1,−2π≤x≤−23π​

Choose the graph which matches the function. - f(x)=−3x2cos⁡5xf ( x ) = - 3 x ^ { 2 } \cos 5 xf(x)=−3x2cos5x

Determine whether the graph of f(x) is a sinusoid. - f(x)=18sin⁡πx−16cos⁡πxf ( x ) = 18 \sin \pi x - 16 \cos \pi xf(x)=18sinπx−16cosπx

Evaluate without using a calculator by using ratios in a reference triangle. - sin⁡5π3\sin \frac { 5 \pi } { 3 }sin35π​

Find the angle in degrees that describes the compass bearing. - SE\mathrm { SE }SE

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - cos⁡−1(0.68)\cos ^ { - 1 } ( 0.68 )cos−1(0.68)

Choose the graph which matches the function. - f(x)=3−xcos⁡4xf ( x ) = 3 ^ { - x } \cos 4 xf(x)=3−xcos4x

Solve the problem. -The radius of a car wheel is 13 inches. How many revolutions per minute is the wheel making when the car is travelling at 45mph45 \mathrm { mph }45mph . Round your answer to the nearest revolution.

Give the exact value. - csc⁡60∘\csc 60 ^ { \circ }csc60∘

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

Find the specified quantity. -Find the phase shift of $y = 4 - 2 \sin \left( 3 x + \frac { \pi } { 2 } \right)$

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

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant III, $\tan t$

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. - $y = 6 \cos x$

Analyze the function for domain, range, continuity, increasing or decreasing behavior, symmetry, boundedness, extrema, asymptotes, and end behavior. - $f ( x ) = - 3 \tan ^ { - 1 } x$

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = 5 \cos x + 2 \sin x$

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

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 15,20 )$ ; find $\csc \theta$ .

Solve the equation. -Solve $\sin \theta = \frac { \sqrt { 3 } } { 2 }$ for $\theta$ , where $0 \leq \theta \leq \frac { \pi } { 2 }$ .

Solve for x in the given interval. - $\cot x = 1 , - 2 \pi \leq x \leq - \frac { 3 \pi } { 2 }$

Choose the graph which matches the function. - $f ( x ) = - 3 x ^ { 2 } \cos 5 x$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 18 \sin \pi x - 16 \cos \pi x$

Evaluate without using a calculator by using ratios in a reference triangle. - $\sin \frac { 5 \pi } { 3 }$

Find the angle in degrees that describes the compass bearing. - $\mathrm { SE }$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\cos ^ { - 1 } ( 0.68 )$

Choose the graph which matches the function. - $f ( x ) = 3 ^ { - x } \cos 4 x$

Solve the problem. -The radius of a car wheel is 13 inches. How many revolutions per minute is the wheel making when the car is travelling at $45 \mathrm { mph }$ . Round your answer to the nearest revolution.

Give the exact value. - $\csc 60 ^ { \circ }$