Exam 7: The Circular Functions and Their Graphs

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

Solve the problem -The radius of the tires of a car is 20 inches, and they are revolving at the rate of 726 revolutions per minute. How fast is the car traveling in miles per hour?

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

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Suppose the tip of the minute hand of a clock is $2 \mathrm { in }$ . from the center of the clock. Determine the distance traveled by the tip of the minute hand in $3 \frac { 1 } { 2 }$ hours. Give an exact answer.

Find the specified quantity. -Find the period of $y = - 5 \cos \left( 3 x + \frac { \pi } { 2 } \right)$

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. - $\mathrm { r } = 57.84 \text { in.; } \theta = 60 ^ { \circ }$

Find the specified quantity. -Find the period of $y = 2 \cos \left( \frac { 1 } { 3 } x + \frac { \pi } { 3 } \right)$

Solve the problem -Find $\mathrm { v }$ for the tip of the hour hand of a clock, if the hand is $5 \mathrm {~cm}$ long.

Solve the problem -Let angle POQ be designated $\theta$ . Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 48 ^ { \circ }$ , find the length of OU accurate to four decimal places.

Determine the equation of the graph. -

Graph the function over a one-period interval. - $y = 3 + \frac { 1 } { 3 } \sin ( 2 x - \pi )$

Graph the function. - $y=2 \sin x$

Match the function with its graph. -1) $y = - \tan \left( x - \frac { \pi } { 2 } \right)$ 2) $y = \tan \left( x + \frac { \pi } { 2 } \right)$ 3) $y = - \cot \left( x - \frac { \pi } { 2 } \right)$ 4) $y = \cot \left( x + \frac { \pi } { 2 } \right)$

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 sensor light installed on the edge of a home can detect motion for a distance of $44 \mathrm { ft }$ . in front and with a range of motion of $254 ^ { \circ }$ . Over what area will the sensor detect motion and become illuminated? Round to the nearest hundredth.

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\csc 0.2878$

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

Find the phase shift of the function. - $y = - 4 + 3 \sin \left( 4 x - \frac { \pi } { 2 } \right)$

Graph the function over a one-period interval. -Suppose that the average monthly low temperatures for a small town are shown in the table. Month 1 2 3 4 5 6 7 8 9 10 11 12 Temperature 19 27 38 45 57 62 65 58 51 41 33 25 Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$ .

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

Find the specified quantity. -Find the vertical translation of $y = - 4 + 3 \sin \left( 4 x + \frac { \pi } { 6 } \right)$ .