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. - $\mathrm { r } = 4 \mathrm {~cm} , \omega = \frac { \pi } { 3 }$ radian per sec

Solve the problem - $s = \frac { \pi } { 11 } m , r = 7 \mathrm {~m} , \mathrm { t } = 4 \mathrm { sec }$

Give the amplitude or period as requested. -Period of $y = \cos 5 x$

Determine the equation of the graph. -A guitar string is plucked so that it vibrates with a frequency of $\mathrm { F } = 60$ . Suppose the maximum displacement at the center of the string is $\mathrm { s } ( 0 ) = 0.54$ . Find an equation of the form $\mathrm { s } ( \mathrm { t } ) = \mathrm { a } \cos \mathrm { bt }$ to model this displacement. Round constants to 2 decimal places.

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

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $- 270 ^ { \circ }$

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

Graph the function over a one-period interval. -Tides go up and down in a 13.2-hour period. The average depth of a certain river is $11 \mathrm {~m}$ and ranges from 6 to $16 \mathrm {~m}$ . The variation can be approximated by a sine curve. Write an equation that gives the approximate variation $\mathrm { y }$ , if $\mathrm { x }$ is the number of hours after midnight and high tide occurs at 8:00 am.

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

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. - $\mathrm { r } = 4.0 \mathrm { ft } , \theta = \frac { 2 \pi } { 3 }$ radians

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

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Find the distance between City $\mathrm { E } , 53 ^ { \circ } \mathrm { N }$ and City F, $55 ^ { \circ } \mathrm { S }$ . (Round to the nearest kilometer.)

Describe how an angle measure can be converted from degrees to radians.

Find the value of s in the interval [ $[ 0 , \pi / 2 ]$ /2] that makes the statement true. Round to four decimal places. - $\csc s = 2.6819$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $14.24 ^ { \circ }$

Convert the degree measure to radians. Leave answer as a multiple of $\pi .$ - $- 670 ^ { \circ }$

Determine the equation of the graph. -Write the equation that describes the simple harmonic motion of a particle moving uniformly around a circle of radius 8 units, with angular speed 3 radians per second.

Match the function with its graph. -1) $y = \sec x$ 2) $y = \csc x$ 3) $y = - \sec x$ 4) $y = - \csc x$

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $33 ^ { \circ } 19 ^ { \prime }$

Graph the function over a one-period interval. -Use regression to find constants $a , b , c$ , and $d$ so that $f ( x ) = a \sin ( b x + c ) + d$ models the data give below. Round all answers to 9 decimal places. Month 1 2 3 4 5 6 7 8 9 10 11 12 Precipitation (inches) 1 3 6 9 11 12 11 9 7 5 3 2