Exam 7: The Circular Functions and Their Graphs

Use the formula v $v = r \omega$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 290.8 \mathrm {~m}$ per sec, $\omega = 0.29226$ radian per sec (Round to four decimal places when necessary.)

(Multiple Choice)

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Question 221

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 3 \pi } { 4 }$

(Multiple Choice)

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Question 222

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin \frac { 1 } { 3 } x$

(Multiple Choice)

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Question 223

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = \frac { \pi } { 4 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

(Multiple Choice)

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Question 224

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. -A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if the central angle, $\theta = 20 ^ { \circ }$ and the radius, $r = 160$ meters. Round to the nearest whole number.

(Multiple Choice)

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Question 225

Find the exact circular function value. - $\cos \frac { - 2 \pi } { 3 }$

(Multiple Choice)

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Question 226

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

(Multiple Choice)

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Question 227

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $338 ^ { \circ } 32 ^ { \prime }$

(Multiple Choice)

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Question 228

Determine the equation of the graph. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

(Multiple Choice)

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Question 229

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 2 }$

(Multiple Choice)

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Question 230

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 231

Graph the function. - $y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$

(Multiple Choice)

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Question 232

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

(Multiple Choice)

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Question 233

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 8 \pi } { 5 }$

(Multiple Choice)

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Question 234

Solve the problem -Find $\omega$ for a spoke on a bike tire revolving 99 times per minute.

(Multiple Choice)

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Question 235

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

(Multiple Choice)

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Question 236

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. -A circular sector has an area of $384 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?

(Multiple Choice)

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Question 237

Graph the function. - $y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$

(Multiple Choice)

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Question 238

Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

(Multiple Choice)

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Question 239

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } s = \frac { 1 } { 3 }$

(Multiple Choice)

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Question 240

Showing 221 - 240 of 286

Use the formula v $v = r \omega$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 290.8 \mathrm {~m}$ per sec, $\omega = 0.29226$ radian per sec (Round to four decimal places when necessary.)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 3 \pi } { 4 }$

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin \frac { 1 } { 3 } x$

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = \frac { \pi } { 4 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

Find the exact circular function value. - $\cos \frac { - 2 \pi } { 3 }$

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

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $338 ^ { \circ } 32 ^ { \prime }$

Determine the equation of the graph. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 2 }$

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. - $y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 8 \pi } { 5 }$

Solve the problem -Find $\omega$ for a spoke on a bike tire revolving 99 times per minute.

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

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. -A circular sector has an area of $384 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?

Graph the function. - $y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$

Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } s = \frac { 1 } { 3 }$

Review of Basic Concepts

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

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Exam 7: The Circular Functions and Their Graphs

Use the formula v v=rωv = r \omegav=rω to find the value of the missing variable. Give an exact answer unless otherwise indicated. - v=290.8 m\mathrm { v } = 290.8 \mathrm {~m}v=290.8 m per sec, ω=0.29226\omega = 0.29226ω=0.29226 radian per sec (Round to four decimal places when necessary.)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 3π4\frac { 3 \pi } { 4 }43π​

Give the amplitude or period as requested. -Amplitude of y=−2sin⁡13xy = - 2 \sin \frac { 1 } { 3 } xy=−2sin31​x

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=π4\omega = \frac { \pi } { 4 }ω=4π​ radian per min,t=5 min\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}min,t=5 min

Find the exact circular function value. - cos⁡−2π3\cos \frac { - 2 \pi } { 3 }cos3−2π​

Graph the function. - y=−cos⁡πxy = - \cos \pi xy=−cosπx

Convert the degree measure to radians, correct to four decimal places. 3.1416 for π. 3.1416 \text { for } \pi \text {. }3.1416 for π. - 338∘32′338 ^ { \circ } 32 ^ { \prime }338∘32′

Determine the equation of the graph. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is 12\frac { 1 } { 2 }21​ second, determine a trigonometric model that gives the position of the weight at time ttt seconds.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - −π2- \frac { \pi } { 2 }−2π​

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=12tan⁡(35x−π6)y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)y=21​tan(53​x−6π​)

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - 8π5\frac { 8 \pi } { 5 }58π​

Solve the problem -Find ω\omegaω for a spoke on a bike tire revolving 99 times per minute.

Graph the function. - y=cos⁡(x+π2)y = \cos \left( x + \frac { \pi } { 2 } \right)y=cos(x+2π​)

Find the area of a sector of a circle having radius r and central angle θ\thetaθ . If necessary, express the answer to the nearest tenth. -A circular sector has an area of 384ft2384 \mathrm { ft } ^ { 2 }384ft2 . The radius of the circle is 8 feet. What is the arc length of the sector?

Graph the function. - y=23tan⁡(12x+π6)y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)y=32​tan(21​x+6π​)

Find the exact circular function value. - tan⁡7π6\tan \frac { 7 \pi } { 6 }tan67π​

Find the exact values of s in the given interval that satisfy the given condition. - [0,2π);tan⁡2s=13[ 0,2 \pi ) ; \tan ^ { 2 } s = \frac { 1 } { 3 }[0,2π);tan2s=31​

Review of Basic Concepts

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

Filters

Use the formula v $v = r \omega$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 290.8 \mathrm {~m}$ per sec, $\omega = 0.29226$ radian per sec (Round to four decimal places when necessary.)

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 3 \pi } { 4 }$

Give the amplitude or period as requested. -Amplitude of $y = - 2 \sin \frac { 1 } { 3 } x$

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = \frac { \pi } { 4 }$ radian per $\mathrm { min } , \mathrm { t } = 5 \mathrm {~min}$

Find the exact circular function value. - $\cos \frac { - 2 \pi } { 3 }$

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

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $338 ^ { \circ } 32 ^ { \prime }$

Determine the equation of the graph. -A weight attached to a spring is pulled down 6 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 2 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { \pi } { 2 }$

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. - $y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{1}{2} \tan \left(\frac{3}{5} x-\frac{\pi}{6}\right)$

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 8 \pi } { 5 }$

Solve the problem -Find $\omega$ for a spoke on a bike tire revolving 99 times per minute.

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

Find the area of a sector of a circle having radius r and central angle $\theta$ . If necessary, express the answer to the nearest tenth. -A circular sector has an area of $384 \mathrm { ft } ^ { 2 }$ . The radius of the circle is 8 feet. What is the arc length of the sector?

Graph the function. - $y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$ $Graph the function. - y=\frac{2}{3} \tan \left(\frac{1}{2} x+\frac{\pi}{6}\right)$

Find the exact circular function value. - $\tan \frac { 7 \pi } { 6 }$

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; \tan ^ { 2 } s = \frac { 1 } { 3 }$