Exam 7: The Circular Functions and Their Graphs

Determine the equation of the graph. -The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi t$ 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? Round values to two decimal places, if necessary.

Is it correct to say that the value of ta $\tan 45 = 1$ ? Explain your answer.

Graph the function. - $y = \frac { 1 } { 2 } \sec \left( \frac { 3 } { 5 } x + \frac { \pi } { 4 } \right)$

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. -A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the frequency of the system is $\frac { 5 } { \pi }$ cycles per second, determine a trigonometric model that gives the position of the weight at time $t$ second.

Solve the problem -Two pulleys of diameters $6 \mathrm {~m}$ and $3 \mathrm {~m}$ are connected by a belt. The larger pulley rotates 31 times per min. Find the angular speed of the smaller pulley.

Find the specified quantity. -Find the period of $y = - 5 \sin \left( \frac { 1 } { 3 } x - \frac { \pi } { 2 } \right)$ .

Solve the problem -A wheel is rotating at 8 radians per sec, and the wheel has a 56 -inch diameter. To the nearest foot per minute, what is the speed of a point on the rim?

Give the amplitude or period as requested. -Amplitude of $y = - 5 \sin 2 x$

Use a table or a calculator to evaluate the function. Round to four decimal places. - $\cos 0.2305$

Graph the function. - $y = \frac { 1 } { 2 } \cot \left( \frac { 1 } { 2 } x + \frac { \pi } { 4 } \right)$

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

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. -The chart represents the amount of fuel consumed by a machine used in manufacturing. The machine is turned on at the beginning of the day, takes a certain amount of time to reach its full power (the point at which it uses the most fuel per hour), runs for a certain number of hours, and is shut off at the end of the work day. The fuel usage per hour of the machine is represented by a periodic function. What is the period in hours of this function?

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 $\sin \theta$

Find the value of s in the interval [ $[ 0 , \pi / 2 ]$ /2] that makes the statement true. Round to four decimal places. - $\sec s = 6.8958$

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. -

Find the exact values of s in the given interval that satisfy the given condition. - $[ - \pi , \pi ) ; 2 \cos ^ { 2 } \mathrm {~s} = 1$

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

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

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

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 $\cos \theta$ .