Exam 6: The Circular Functions and Their Graphs

Solve the problem. -Let angle POQ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 45 ^ { \circ }$ , find the exact length of $O V$ . $Solve the problem. -Let angle POQ be designated \theta . Angles P Q R and VRQ are right angles. If \theta = 45 ^ { \circ } , find the exact length of O V .$

(Multiple Choice)

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Question 221

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 60 ^ { \circ }$

(Multiple Choice)

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Question 222

Solve the problem. -Let angle POQ be designated $\theta$ . Angles $P Q R$ and VRQ are right angles. If $\theta = 69 ^ { \circ }$ , find the length of $O Q$ accurate to four decimal places. $Solve the problem. -Let angle POQ be designated \theta . Angles P Q R and VRQ are right angles. If \theta = 69 ^ { \circ } , find the length of O Q accurate to four decimal places.$

(Multiple Choice)

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Question 223

Find the exact circular function value. - $\sin \frac { 3 \pi } { 4 }$

(Multiple Choice)

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Question 224

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find $\sin \theta$ . $The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find \sin \theta .$

(Multiple Choice)

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Question 225

Solve the problem. -A wheel is rotating at 8 radians per sec, and the wheel has a 51 -inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?

(Multiple Choice)

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Question 226

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $35 ^ { \circ } 25 ^ { \prime }$

(Multiple Choice)

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Question 227

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3.5$ hours. Give an exact answer.

(Multiple Choice)

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Question 228

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $13 \pi$

(Multiple Choice)

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Question 229

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 2 } } { 2 }$

(Multiple Choice)

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Question 230

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }$

(Multiple Choice)

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Question 231

Graph the function over a one-period interval. - $y=4+\sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=4+\sin (2 x-\pi) \$ \

(Multiple Choice)

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Question 232

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

(Multiple Choice)

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Question 233

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 447.7 \mathrm {~m}$ per sec, $\omega = 0.2374$ radian per sec (Round to four decimal places when necessary.)

(Multiple Choice)

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Question 234

Solve the problem. -A wheel with a 32 -inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 11 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

(Multiple Choice)

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Question 235

Graph the function. - $y=1-2 \cos x$ $Graph the function. - y=1-2 \cos x$

(Multiple Choice)

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Question 236

Solve the problem. -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 13 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

(Multiple Choice)

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Question 237

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find $\tan \theta$ . $The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find \tan \theta .$

(Multiple Choice)

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Question 238

Graph the function. - $y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$ $Graph the function. - y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$

(Multiple Choice)

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Question 239

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = 1.8600$ radians per min, $\theta = 19.44$ radians (Round to four decimal places when necessary.)

(Multiple Choice)

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Question 240

Showing 221 - 240 of 289

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 60 ^ { \circ }$

Find the exact circular function value. - $\sin \frac { 3 \pi } { 4 }$

Solve the problem. -A wheel is rotating at 8 radians per sec, and the wheel has a 51 -inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $35 ^ { \circ } 25 ^ { \prime }$

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3.5$ hours. Give an exact answer.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $13 \pi$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 2 } } { 2 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }$

Graph the function over a one-period interval. - $y=4+\sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=4+\sin (2 x-\pi) \$ \

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

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 447.7 \mathrm {~m}$ per sec, $\omega = 0.2374$ radian per sec (Round to four decimal places when necessary.)

Solve the problem. -A wheel with a 32 -inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 11 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

Graph the function. - $y=1-2 \cos x$ $Graph the function. - y=1-2 \cos x$

Solve the problem. -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 13 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Graph the function. - $y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$ $Graph the function. - y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = 1.8600$ radians per min, $\theta = 19.44$ radians (Round to four decimal places when necessary.)

Equations and Inequalities

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Exam 6: The Circular Functions and Their Graphs

Solve the problem. -Let angle POQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=45∘\theta = 45 ^ { \circ }θ=45∘ , find the exact length of OVO VOV .

Convert the degree measure to radians. Leave answer as a multiple of π. - −60∘- 60 ^ { \circ }−60∘

Solve the problem. -Let angle POQ be designated θ\thetaθ . Angles PQRP Q RPQR and VRQ are right angles. If θ=69∘\theta = 69 ^ { \circ }θ=69∘ , find the length of OQO QOQ accurate to four decimal places.

Find the exact circular function value. - sin⁡3π4\sin \frac { 3 \pi } { 4 }sin43π​

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find sin⁡θ\sin \thetasinθ .

Solve the problem. -A wheel is rotating at 8 radians per sec, and the wheel has a 51 -inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - 35∘25′35 ^ { \circ } 25 ^ { \prime }35∘25′

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in 3.53.53.5 hours. Give an exact answer.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 13π13 \pi13π

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);cos⁡s=−22[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 2 } } { 2 }[0,2π);coss=−22​​

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);sin⁡s=32[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }[0,2π);sins=23​​

Graph the function over a one-period interval. - y=4+sin⁡(2x−π)y=4+\sin (2 x-\pi)y=4+sin(2x−π) \

Graph the function. - y=2+cot⁡xy=2+\cot xy=2+cotx

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - v=447.7 m\mathrm { v } = 447.7 \mathrm {~m}v=447.7 m per sec, ω=0.2374\omega = 0.2374ω=0.2374 radian per sec (Round to four decimal places when necessary.)

Solve the problem. -A wheel with a 32 -inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 11 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

Graph the function. - y=1−2cos⁡xy=1-2 \cos xy=1−2cosx

Solve the problem. -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 13 seconds a central angle of 15\frac { 1 } { 5 }51​ radian has been covered, what is the angular speed of the ball?

The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the indicated circular function value of θ. -Find tan⁡θ\tan \thetatanθ .

Graph the function. - y=−23sin⁡(x−π4)y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)y=−32​sin(x−4π​)

Use the formula ω=θt\omega = \frac { \theta } { t }ω=tθ​ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - ω=1.8600\omega = 1.8600ω=1.8600 radians per min, θ=19.44\theta = 19.44θ=19.44 radians (Round to four decimal places when necessary.)

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

Convert the degree measure to radians. Leave answer as a multiple of π. - $- 60 ^ { \circ }$

Find the exact circular function value. - $\sin \frac { 3 \pi } { 4 }$

Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π. - $35 ^ { \circ } 25 ^ { \prime }$

Solve the problem. -Suppose the tip of the minute hand of a clock is 9 inches from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3.5$ hours. Give an exact answer.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $13 \pi$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \cos s = - \frac { \sqrt { 2 } } { 2 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \sin \mathrm { s } = \frac { \sqrt { 3 } } { 2 }$

Graph the function over a one-period interval. - $y=4+\sin (2 x-\pi)$ $Graph the function over a one-period interval. - y=4+\sin (2 x-\pi) \$ \

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

Use the formula v = rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 447.7 \mathrm {~m}$ per sec, $\omega = 0.2374$ radian per sec (Round to four decimal places when necessary.)

Graph the function. - $y=1-2 \cos x$ $Graph the function. - y=1-2 \cos x$

Solve the problem. -A ball on the end of a string is spinning around a circle with a radius of 5 centimeters. If in 13 seconds a central angle of $\frac { 1 } { 5 }$ radian has been covered, what is the angular speed of the ball?

Graph the function. - $y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$ $Graph the function. - y=-\frac{2}{3} \sin \left(x-\frac{\pi}{4}\right)$

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = 1.8600$ radians per min, $\theta = 19.44$ radians (Round to four decimal places when necessary.)