Exam 7: The Circular Functions and Their Graphs

The function graphed is of the form y $y = a \tan b x \text { or } y = a \cot b x , \text { where } b > 0 \text {. }$ etermine the equation of the graph. -

Give the amplitude or period as requested. -Amplitude of $y = 5 \cos \frac { 1 } { 4 } x$

Determine the equation of the graph. -The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 3 \cos 5 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. When does the weight first reach its maximum height?

Use the formula v $v = r \omega$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\mathrm { v } = 10 \mathrm { ft }$ per sec, $\mathrm { r } = 5.0 \mathrm { ft }$ (Round to four decimal places when necessary.)

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

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

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $\frac { 8 } { 3 } \pi$

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

Find the length of an arc intercepted by a central angle $\theta$ in a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 20.1 \mathrm { ft } ; \theta = \frac { \pi } { 26 }$ radians

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. - $\mathrm { r } = 47.2 \mathrm {~cm} , \theta = \frac { \pi } { 11 }$ radians

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

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

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. -What is the difference in area covered by a single 5 -inch windshield wiper operating with a central angle of $139 ^ { \circ }$ compared to a pair of 5 -inch wipers operating together each having a central angle of $108 ^ { \circ }$ ? Round to the nearest hundredth.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A pulley rotates through $50 ^ { \circ }$ in one minute. How many rotations (to the nearest tenth of a rotation) does the pulley make in an hour?

Graph the function. - $y=3-4 \sec \left(x-\frac{\pi}{6}\right)$

Find the specified quantity. -Find the amplitude of $y = 4 \sin \left( 2 x + \frac { \pi } { 4 } \right)$ .

Find the length of an arc intercepted by a central angle $\theta$ in a circle of radius r. Round your answer to 1 decimal place. - $\mathrm { r } = 8.44 \mathrm {~cm} . ; \theta = \frac { 12 } { 11 } \pi$ radians

The function graphed is of the form $y = \cos x + c , y = \sin x + c , y = \cos ( x - d ) , \text { or } y = \sin ( x - d )$ where d is the least possible positive value. Determine the equation of the graph. -

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