Exam 4: Trigonometric Functions

Solve the problem. -A police helicopter is monitoring the speed of two cars on a straight road. The helicopter is at an altitude of 4000 feet directly above the road. At one instant, the angle of elevation from the first car to the helicopter is 21°, and The angle of elevation from the second car to the helicopter is 17°. How far apart are the two cars to the nearest Foot?

(Multiple Choice)

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Question 461

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

(Essay)

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Question 462

Use a calculator to solve for x in the given interval - $\cot \theta = 0.7615,0 \leq \theta \leq 2 \pi$

(Multiple Choice)

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Question 463

Graph the function. - $y = 2 \cos x$

(Multiple Choice)

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Question 464

Graph the function. - $y=5 \tan x$ $Graph the function. - y=5 \tan x$

(Multiple Choice)

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Question 465

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - 9,2 ) ;$ find $\cot \theta$

(Multiple Choice)

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Question 466

Use a calculator to find the function value to four decimal places. - $\sin 47.2 ^ { \circ }$

(Multiple Choice)

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Question 467

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

(Multiple Choice)

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Question 468

Graph the function. - $y=4 \sin x+\sin 2 x$ $Graph the function. - y=4 \sin x+\sin 2 x$

(Multiple Choice)

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Question 469

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

(Multiple Choice)

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Question 470

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 9 \sin ^ { 2 } x$

(Multiple Choice)

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Question 471

Graph the function. - $y=2 \cos x$ $Graph the function. - y=2 \cos x$

(Multiple Choice)

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Question 472

Evaluate without using a calculator. - $\sec \beta$ , if $\sin \beta = - \frac { \sqrt { 10 } } { 9 }$ , with $\beta$ in quadrant III

(Multiple Choice)

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Question 473

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, $\sin \mathrm { t }$

(Multiple Choice)

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Question 474

Solve the problem. -A ship travels $82 \mathrm {~km}$ on a bearing of $30 ^ { \circ }$ , and then travels on a bearing of $120 ^ { \circ }$ for $117 \mathrm {~km}$ . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

(Multiple Choice)

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Question 475

Provide an appropriate response. -Enter $1.077$ in your calculator and press the keys for inverse sine. Explain why the response will indicate that something is wrong.

(Essay)

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Question 476

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\csc x = 4 \sin x$

(Multiple Choice)

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Question 477

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. -arctan $19.2$

(Multiple Choice)

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Question 478

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

(Multiple Choice)

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Question 479

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $13 ^ { \circ } 44 ^ { \prime }$ . If the dam is 1117 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

(Multiple Choice)

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Question 480

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

Use a calculator to solve for x in the given interval - $\cot \theta = 0.7615,0 \leq \theta \leq 2 \pi$

Graph the function. - $y = 2 \cos x$

Graph the function. - $y=5 \tan x$ $Graph the function. - y=5 \tan x$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - 9,2 ) ;$ find $\cot \theta$

Use a calculator to find the function value to four decimal places. - $\sin 47.2 ^ { \circ }$

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

Graph the function. - $y=4 \sin x+\sin 2 x$ $Graph the function. - y=4 \sin x+\sin 2 x$

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

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 9 \sin ^ { 2 } x$

Graph the function. - $y=2 \cos x$ $Graph the function. - y=2 \cos x$

Evaluate without using a calculator. - $\sec \beta$ , if $\sin \beta = - \frac { \sqrt { 10 } } { 9 }$ , with $\beta$ in quadrant III

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, $\sin \mathrm { t }$

Solve the problem. -A ship travels $82 \mathrm {~km}$ on a bearing of $30 ^ { \circ }$ , and then travels on a bearing of $120 ^ { \circ }$ for $117 \mathrm {~km}$ . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Provide an appropriate response. -Enter $1.077$ in your calculator and press the keys for inverse sine. Explain why the response will indicate that something is wrong.

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\csc x = 4 \sin x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. -arctan $19.2$

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

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $13 ^ { \circ } 44 ^ { \prime }$ . If the dam is 1117 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

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

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

Use a calculator to solve for x in the given interval - cot⁡θ=0.7615,0≤θ≤2π\cot \theta = 0.7615,0 \leq \theta \leq 2 \picotθ=0.7615,0≤θ≤2π

Graph the function. - y=2cos⁡xy = 2 \cos xy=2cosx

Graph the function. - y=5tan⁡xy=5 \tan xy=5tanx

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(−9,2);\mathrm { P } ( - 9,2 ) ;P(−9,2); find cot⁡θ\cot \thetacotθ

Use a calculator to find the function value to four decimal places. - sin⁡47.2∘\sin 47.2 ^ { \circ }sin47.2∘

Graph the function. - y=−csc⁡(x4)y=-\csc \left(\frac{x}{4}\right)y=−csc(4x​)

Graph the function. - y=4sin⁡x+sin⁡2xy=4 \sin x+\sin 2 xy=4sinx+sin2x

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, cos⁡t\cos tcost

Determine whether the function is periodic. If it is periodic, find the period. - f(x)=9sin⁡2xf ( x ) = 9 \sin ^ { 2 } xf(x)=9sin2x

Graph the function. - y=2cos⁡xy=2 \cos xy=2cosx

Evaluate without using a calculator. - sec⁡β\sec \betasecβ , if sin⁡β=−109\sin \beta = - \frac { \sqrt { 10 } } { 9 }sinβ=−910​​ , with β\betaβ in quadrant III

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, sin⁡t\sin \mathrm { t }sint

Solve the problem. -A ship travels 82 km82 \mathrm {~km}82 km on a bearing of 30∘30 ^ { \circ }30∘ , and then travels on a bearing of 120∘120 ^ { \circ }120∘ for 117 km117 \mathrm {~km}117 km . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Provide an appropriate response. -Enter 1.0771.0771.077 in your calculator and press the keys for inverse sine. Explain why the response will indicate that something is wrong.

Find approximate solutions for the equation in the interval −π<X<π -\pi<\mathbf{X}<\pi −π<X<π . Round to three decimal places. - csc⁡x=4sin⁡x\csc x = 4 \sin xcscx=4sinx

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. -arctan 19.219.219.2

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - sin⁡θ=−12\sin \theta = - \frac { 1 } { 2 }sinθ=−21​ and cos⁡θ<0\cos \theta < 0cosθ<0

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 13∘44′13 ^ { \circ } 44 ^ { \prime }13∘44′ . If the dam is 1117 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?

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

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

Use a calculator to solve for x in the given interval - $\cot \theta = 0.7615,0 \leq \theta \leq 2 \pi$

Graph the function. - $y = 2 \cos x$

Graph the function. - $y=5 \tan x$ $Graph the function. - y=5 \tan x$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( - 9,2 ) ;$ find $\cot \theta$

Use a calculator to find the function value to four decimal places. - $\sin 47.2 ^ { \circ }$

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

Graph the function. - $y=4 \sin x+\sin 2 x$ $Graph the function. - y=4 \sin x+\sin 2 x$

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

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 9 \sin ^ { 2 } x$

Graph the function. - $y=2 \cos x$ $Graph the function. - y=2 \cos x$

Evaluate without using a calculator. - $\sec \beta$ , if $\sin \beta = - \frac { \sqrt { 10 } } { 9 }$ , with $\beta$ in quadrant III

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, $\sin \mathrm { t }$

Solve the problem. -A ship travels $82 \mathrm {~km}$ on a bearing of $30 ^ { \circ }$ , and then travels on a bearing of $120 ^ { \circ }$ for $117 \mathrm {~km}$ . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Provide an appropriate response. -Enter $1.077$ in your calculator and press the keys for inverse sine. Explain why the response will indicate that something is wrong.

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $\csc x = 4 \sin x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. -arctan $19.2$

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

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is $13 ^ { \circ } 44 ^ { \prime }$ . If the dam is 1117 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)?