Exam 6: The Circular Functions and Their Graphs

Write the word or phrase that best completes each statement or answers the question. -Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of radians.

(Short Answer)

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Question 81

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 $4 \mathrm { ft }$ ?

(Multiple Choice)

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Question 82

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $58 ^ { \circ } 9 ^ { \prime }$

(Multiple Choice)

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Question 83

Find the exact values of s in the given interval that satisfy the given condition. - $[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$

(Multiple Choice)

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Question 84

Solve the problem. -A guitar string is plucked so that it vibrates with a frequency of $F = 60$ . Suppose the maximum displacement at the center of the string is $s ( 0 ) = 0.53$ . Find an equation of the form $s ( t ) = a \cos b t$ to model this displacement. Round constants to 2 decimal places.

(Multiple Choice)

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Question 85

Solve the problem. -Each tire of an automobile has a radius of 2 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 105 feet per sec? Round your answer to the nearest tenth.

(Multiple Choice)

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Question 86

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

(Multiple Choice)

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Question 87

Graph the function. - $y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$

(Multiple Choice)

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Question 88

Find the phase shift of the function. - $y = - 5 \cos ( 6 x + \pi )$

(Multiple Choice)

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Question 89

Match the function with its graph. -1) $y = \sin 3 x$ 2) $y = 3 \cos x$ 3) $y = 3 \sin x$ 4) $y = \cos 3 x$ A. $Match the function with its graph. -1) y = \sin 3 x 2) y = 3 \cos x 3) y = 3 \sin x 4) y = \cos 3 x A. B. C. D.$ B. $Match the function with its graph. -1) y = \sin 3 x 2) y = 3 \cos x 3) y = 3 \sin x 4) y = \cos 3 x A. B. C. D.$ C. $Match the function with its graph. -1) y = \sin 3 x 2) y = 3 \cos x 3) y = 3 \sin x 4) y = \cos 3 x A. B. C. D.$ D. $Match the function with its graph. -1) y = \sin 3 x 2) y = 3 \cos x 3) y = 3 \sin x 4) y = \cos 3 x A. B. C. D.$

(Multiple Choice)

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Question 90

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 450 ^ { \circ }$

(Multiple Choice)

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Question 91

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

(Multiple Choice)

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Question 92

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 47 } { 18 } \pi$

(Multiple Choice)

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Question 93

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

(Multiple Choice)

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Question 94

Solve the problem. -Let angle $P O Q$ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 51 ^ { \circ }$ , find the length of OU accurate to four decimal places. $Solve the problem. -Let angle P O Q be designated \theta . Angles P Q R and VRQ are right angles. If \theta = 51 ^ { \circ } , find the length of OU accurate to four decimal places.$

(Multiple Choice)

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Question 95

Convert the degree measure to radians. Leave answer as a multiple of π. - $288 ^ { \circ }$

(Multiple Choice)

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Question 96

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower $450 \mathrm {~m}$ high subtends an angle of $2 ^ { \circ } 10 ^ { \prime }$ . How far away is the tower?

(Multiple Choice)

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Question 97

Graph the function. - $y=3 \cos \left(x+\frac{\pi}{3}\right)$ $Graph the function. - y=3 \cos \left(x+\frac{\pi}{3}\right)$

(Multiple Choice)

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Question 98

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$

(Multiple Choice)

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Question 99

Solve the problem. -A circular sector has an area of $128 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?

(Multiple Choice)

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Question 100

Showing 81 - 100 of 289

Write the word or phrase that best completes each statement or answers the question. -Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of radians.

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 $4 \mathrm { ft }$ ?

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $58 ^ { \circ } 9 ^ { \prime }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$

Solve the problem. -A guitar string is plucked so that it vibrates with a frequency of $F = 60$ . Suppose the maximum displacement at the center of the string is $s ( 0 ) = 0.53$ . Find an equation of the form $s ( t ) = a \cos b t$ to model this displacement. Round constants to 2 decimal places.

Solve the problem. -Each tire of an automobile has a radius of 2 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 105 feet per sec? Round your answer to the nearest tenth.

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$

Find the phase shift of the function. - $y = - 5 \cos ( 6 x + \pi )$

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 450 ^ { \circ }$

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 47 } { 18 } \pi$

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

Convert the degree measure to radians. Leave answer as a multiple of π. - $288 ^ { \circ }$

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower $450 \mathrm {~m}$ high subtends an angle of $2 ^ { \circ } 10 ^ { \prime }$ . How far away is the tower?

Graph the function. - $y=3 \cos \left(x+\frac{\pi}{3}\right)$ $Graph the function. - y=3 \cos \left(x+\frac{\pi}{3}\right)$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$

Solve the problem. -A circular sector has an area of $128 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?

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Polynomial and Rational Functions

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Exam 6: The Circular Functions and Their Graphs

Write the word or phrase that best completes each statement or answers the question. -Find the value of the arc length when θ\thetaθ (the central Angle) is given in degrees instead of radians.

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 4ft4 \mathrm { ft }4ft ?

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 58∘9′58 ^ { \circ } 9 ^ { \prime }58∘9′

Find the exact values of s in the given interval that satisfy the given condition. - [−2π,π);cos⁡2 s=34[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }[−2π,π);cos2 s=43​

Solve the problem. -Each tire of an automobile has a radius of 2 feet. How many revolutions per minute (rpm) does a tire make when the automobile is traveling at a speed of 105 feet per sec? Round your answer to the nearest tenth.

Find the exact value of s in the given interval that has the given circular function value. - [π,3π2];sin⁡s=−32\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }[π,23π​];sins=−23​​

Graph the function. - y=−23csc⁡(23x−π2)y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)y=−32​csc(32​x−2π​)

Find the phase shift of the function. - y=−5cos⁡(6x+π)y = - 5 \cos ( 6 x + \pi )y=−5cos(6x+π)

Match the function with its graph. -1) y=sin⁡3xy = \sin 3 xy=sin3x 2) y=3cos⁡xy = 3 \cos xy=3cosx 3) y=3sin⁡xy = 3 \sin xy=3sinx 4) y=cos⁡3xy = \cos 3 xy=cos3x A. B. C. D.

Convert the degree measure to radians. Leave answer as a multiple of π. - −450∘- 450 ^ { \circ }−450∘

Find the phase shift of the function. - y=3sin⁡(x−π4)y = 3 \sin \left( x - \frac { \pi } { 4 } \right)y=3sin(x−4π​)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −4718π- \frac { 47 } { 18 } \pi−1847​π

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

Solve the problem. -Let angle POQP O QPOQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=51∘\theta = 51 ^ { \circ }θ=51∘ , find the length of OU accurate to four decimal places.

Convert the degree measure to radians. Leave answer as a multiple of π. - 288∘288 ^ { \circ }288∘

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower 450 m450 \mathrm {~m}450 m high subtends an angle of 2∘10′2 ^ { \circ } 10 ^ { \prime }2∘10′ . How far away is the tower?

Graph the function. - y=3cos⁡(x+π3)y=3 \cos \left(x+\frac{\pi}{3}\right)y=3cos(x+3π​)

Find the exact value of s in the given interval that has the given circular function value. - [π,3π2];tan⁡s=1\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1[π,23π​];tans=1

Solve the problem. -A circular sector has an area of 128ft2128 \mathrm { ft } ^ { 2 }128ft2 . The radius of the circle is 8 feet. What is the arc length of the sector?

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Write the word or phrase that best completes each statement or answers the question. -Find the value of the arc length when $\theta$ (the central Angle) is given in degrees instead of radians.

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 $4 \mathrm { ft }$ ?

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $58 ^ { \circ } 9 ^ { \prime }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ - 2 \pi , \pi ) ; \cos ^ { 2 } \mathrm {~s} = \frac { 3 } { 4 }$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \sin \mathrm { s } = - \frac { \sqrt { 3 } } { 2 }$

Graph the function. - $y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$ $Graph the function. - y=-\frac{2}{3} \csc \left(\frac{2}{3} x-\frac{\pi}{2}\right)$

Find the phase shift of the function. - $y = - 5 \cos ( 6 x + \pi )$

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 450 ^ { \circ }$

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 47 } { 18 } \pi$

Convert the degree measure to radians. Leave answer as a multiple of π. - $288 ^ { \circ }$

Approximate the length using the formula for arc length. Round to the nearest meter. -A television tower $450 \mathrm {~m}$ high subtends an angle of $2 ^ { \circ } 10 ^ { \prime }$ . How far away is the tower?

Graph the function. - $y=3 \cos \left(x+\frac{\pi}{3}\right)$ $Graph the function. - y=3 \cos \left(x+\frac{\pi}{3}\right)$

Find the exact value of s in the given interval that has the given circular function value. - $\left[ \pi , \frac { 3 \pi } { 2 } \right] ; \tan \mathrm { s } = 1$

Solve the problem. -A circular sector has an area of $128 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?