Exam 7: The Circular Functions and Their Graphs

Solve the problem -A wheel is rotating at 7 radians/sec, and the wheel has a 48 -inch diameter. To the nearest foot, what is the speed of a point on the rim in $\mathrm { ft } / \mathrm { min }$ ?

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 US.

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 $\csc \theta$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A wheel with a 32 -inch radius is marked at two points on the rim. The distance between the marks along the wheel is found to be 16 inches. What is the angle (to the nearest tenth of a degree) between the radii to the two marks?

Find the exact values of s in the given interval that satisfy the given condition. - $[ 0,2 \pi ) ; 4 \sin ^ { 2 } s = 3$

Find the phase shift of the function. - $y = - 5 \cos ( 2 x + \pi )$

Solve the problem -Let angle POQ be designated $\theta$ . Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 50 ^ { \circ }$ , find the length of US accurate to four decimal places.

Find the value of s in the interval [ $[ 0 , \pi / 2 ]$ /2] that makes the statement true. Round to four decimal places. - $\sin \mathrm { s } = 0.2336$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A pendulum swinging through a central angle of $76 ^ { \circ }$ completes an arc of length $14.3 \mathrm {~cm}$ . What is the length of the pendulum? Round to the nearest hundredth.

Convert the radian measure to degrees. Round to the nearest hundredth if necessary. - $- \frac { 7 \pi } { 4 }$

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

Solve the problem -Let angle POQ be designated $\theta$ . Angles $\mathrm { PQR }$ and VRQ are right angles. If $\theta = 18 ^ { \circ }$ , find the length OV accurate to four decimal places.

Find the phase shift of the function. - $y = 2 - 2 \sin \left( 6 x + \frac { \pi } { 4 } \right)$

Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km. -A pendulum of length $17.0$ inches swings $1 ^ { \circ } 6 ^ { \prime }$ to each side of its vertical position. What is the length (to the nearest hundredth of an inch) of the arc through which the end of the pendulum swings?

Convert the degree measure to radians, correct to four decimal places. $3.1416 \text { for } \pi \text {. }$ - $36 ^ { \circ }$

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 $O Q$ .

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

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. -The voltage $\mathrm { E }$ in an electrical circuit is given by $\mathrm { E } = 7.7 \cos 180 \pi \mathrm { t }$ , where $\mathrm { t }$ is time measured in seconds. Find the period.

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 $14 \mathrm { in } ^ { 2 }$ and an arc length of 3 inches. What is the measure of the central angle in degrees? Round to the nearest degree.

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. -The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 8 \cos 20 \pi \mathrm { t }$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?