91Ó°ÊÓ

Complete the following table for the given functions and then plot the resulting graphs. $$\begin{array}{c|c|c|c|c|c|c|c|c|c} x & -\pi & -\frac{3 \pi}{4} & -\frac{\pi}{2} & -\frac{\pi}{4} & 0 & \frac{\pi}{4} & \frac{\pi}{2} & \frac{3 \pi}{4} & \pi \\ \hline y & & & & & & & & & \end{array}$$ $$\begin{array}{c|c|c|c|c|c|c|c|c} x & \frac{5 \pi}{4} & \frac{3 \pi}{2} & \frac{7 \pi}{4} & 2 \pi & \frac{9 \pi}{4} & \frac{5 \pi}{2} & \frac{11 \pi}{4} & 3 \pi \\ \hline y & & & & & & & & \end{array}$$ $$y=\cos x$$

Solve the given problems. If the period is \(\frac{1}{10} \mathrm{s},\) find \(f\)

Complete the following table for the given functions and then plot the resulting graphs. $$\begin{array}{c|c|c|c|c|c|c|c|c|c} x & -\pi & -\frac{3 \pi}{4} & -\frac{\pi}{2} & -\frac{\pi}{4} & 0 & \frac{\pi}{4} & \frac{\pi}{2} & \frac{3 \pi}{4} & \pi \\ \hline y & & & & & & & & & \end{array}$$ $$\begin{array}{c|c|c|c|c|c|c|c|c} x & \frac{5 \pi}{4} & \frac{3 \pi}{2} & \frac{7 \pi}{4} & 2 \pi & \frac{9 \pi}{4} & \frac{5 \pi}{2} & \frac{11 \pi}{4} & 3 \pi \\ \hline y & & & & & & & & \end{array}$$ $$y=-3 \cos x$$

Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. $$y=\cos \left(x+\frac{\pi}{6}\right)$$

Find the amplitude and period of each function and then sketch its graph. $$y=3 \cos 8 x$$

Sketch the curves of the given functions by addition of ordinates. $$y=\frac{1}{10} x^{2}-\sin \pi x$$

Solve the given problems. If \(\omega=40 \pi \mathrm{rad} / \mathrm{s},\) find the period.

Solve the given problems. If the period is \(\frac{1}{5} \mathrm{s},\) find \(\omega\)

Sketch the curves of the given functions by addition of ordinates. $$y=\frac{1}{4} x^{2}+\cos 3 x$$

Complete the following table for the given functions and then plot the resulting graphs. $$\begin{array}{c|c|c|c|c|c|c|c|c|c} x & -\pi & -\frac{3 \pi}{4} & -\frac{\pi}{2} & -\frac{\pi}{4} & 0 & \frac{\pi}{4} & \frac{\pi}{2} & \frac{3 \pi}{4} & \pi \\ \hline y & & & & & & & & & \end{array}$$ $$\begin{array}{c|c|c|c|c|c|c|c|c} x & \frac{5 \pi}{4} & \frac{3 \pi}{2} & \frac{7 \pi}{4} & 2 \pi & \frac{9 \pi}{4} & \frac{5 \pi}{2} & \frac{11 \pi}{4} & 3 \pi \\ \hline y & & & & & & & & \end{array}$$ $$y=-4 \sin x$$