91Ó°ÊÓ

Give the amplitude and sketch the graphs of the given functions. Check each using a calculator. $$y=-0.4 \cos x$$

$$\text {Plot the Lissajous figures.}$$ $$x=5 \cos t+2, y=5 \sin t-3$$

Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. $$y=360 \cos (6 \pi x-3)$$

Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. $$y=\sin \left(\pi^{2} x-\pi\right)$$

$$\text {Plot the Lissajous figures.}$$$$\text {Plot the Lissajous figures.}$$ $$x=2 \sin t, y=3 \sin t$$

Sketch the required curves. The rotating beacon of a parked police car is 12 m from a straight wall. (a) Sketch the graph of the length \(L\) of the light beam, where \(L=12 \sec \pi t,\) for \(0 \leq t \leq 2.0 \mathrm{s} .\) (b) Which part(s) of the graph show meaningful values? Explain.

View at least two cycles of the graphs of the given functions on a calculator. $$y=75 \tan \left(0.5 x-\frac{\pi}{16}\right)$$

Although units of \(\pi\) are convenient, we must remember that \(\pi\) is only a number. Numbers that are not multiples of \(\pi\) may be used. Plot the indicated graphs by finding the values of \(y\) that correspond to values of \(x\) of \(0,1,2,3,4,5,6,\) and 7 on a calculator. (Remember, the numbers \(0,1,2,\) and so on represent radian measure.) $$y=\sin x$$

The period is given for a function of the form \(y=\sin b x .\) Write the function corresponding to the given period. $$\frac{\pi}{3}$$

Although units of \(\pi\) are convenient, we must remember that \(\pi\) is only a number. Numbers that are not multiples of \(\pi\) may be used. Plot the indicated graphs by finding the values of \(y\) that correspond to values of \(x\) of \(0,1,2,3,4,5,6,\) and 7 on a calculator. (Remember, the numbers \(0,1,2,\) and so on represent radian measure.) $$y=-30 \sin x$$