Exam 7: The Circular Functions and Their Graphs

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 VR.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is $6.6$ centimeters and the radius of the larger wheel is $15.2$ centimeters. Through how many degrees (to the nearest hundredth of a degree) will the larger wheel rotate if the smaller one rotates $38 ^ { \circ }$ ?

Graph the function. - $y = 1 + \sin \left( x - \frac { \pi } { 4 } \right)$

Graph the function. - $y = \frac { 1 } { 3 } \tan 2 x$

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. -

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $71.8396 ^ { \circ }$

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

Solve the problem -Let angle POQ be designated $\theta$ . Angles PQR and VRQ are right angles. If $\theta = 25 ^ { \circ }$ , find the length of VR accurate to four decimal places.

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 $\mathrm { A } , 72 ^ { \circ } \mathrm { N }$ and City B, $57 ^ { \circ } \mathrm { N }$ . (Round to the nearest kilometer.)

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. -

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

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

Solve the problem -Find $\omega$ for the minute hand of a clock.

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -Electrical wire is being wound around a drum with radius of $1.10$ meters. How much line (to the nearest hundredth of a meter) would be wound around the drum if it is rotated through an angle of $270.1 ^ { \circ }$ ?

Use the formula $\omega = \frac { \theta } { t }$ to find the value of the missing variable. Give an exact answer unless otherwise indicated. - $\omega = 7.2935$ radians per min, $\theta = 14.10$ radians (Round to four decimal places when necessary.)

Graph the function over a one-period interval. -Ignoring friction, the time, $\mathrm { t }$ (in seconds), required for a block to slide down an inclined plane is given by the formula $t = \sqrt { \frac { 2 b } { g \sin \theta \cos \theta } }$ where $b$ is the length of the base in feet and $g = 32.2$ feet per second is the acceleration of gravity. How long does it take a block to slide down an inclined plane with a base of 12 feet at an angle of $48 ^ { \circ }$ ? Round your answer to three decimal places.

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

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

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 $\sin \theta$

Graph the function. - $y=\frac{5}{4} \csc \left(\frac{2}{5} x+\frac{\pi}{5}\right)$