Exam 4: Graphs of the Circular Functions

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

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

Find the specified quantity. -Find the period of $y = \sin \left( \frac { 1 } { 4 } x - \frac { \pi } { 2 } \right)$ .

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

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

Find the specified quantity. -Find the vertical translation of $y = - 2 + 2 \sin \left( 3 x + \frac { \pi } { 6 } \right)$ .

Graph the function. - $y = \cos \frac { 3 } { 4 } x$

The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph. -

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

Give the amplitude or period as requested. -Period of $y = \cos x$

Solve the problem. -A weight attached to a spring is pulled down 4 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 $t$ seconds.

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

Use Identities to find the exact value. -A rotating beacon is located 15 ft from a wall. The distance from the beacon to the point on the wall where the beacon is aimed is given by $\mathrm { a } = 15 | \sec 2 \pi \mathrm { t } |$ , where $t$ is time measured in seconds since the beacon started rotating. Find a for $t = 0.42$ seconds. Round your answer to the nearest hundredth.

Determine the equation of the graph. -

Solve the problem. -A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 5 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Graph the function. - $y=-2+\cot x$

Solve the problem. -The formula for the up and down motion of a weight on a spring is given by $s ( t ) = \sin \sqrt { \frac { k } { m } } t$ . If the spring constant is 5 , then what mass $m$ must be used in order to produce a period of 6 seconds?

Graph the function. - $y=-\cos \pi x$

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

Match the function with its graph. -1) $y = \sin \frac { 1 } { 2 } x$ 2) $y = \frac { 1 } { 2 } \cos x$ 3) $y = \frac { 1 } { 2 } \sin x$ 4) $y = \cos \frac { 1 } { 2 } x$ a) b) c) d)