91Ó°ÊÓ

Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the ficnctions. Check each using a calculator. $$y=3 \sin \left(x+\frac{\pi}{4}\right)$$

find the period of each function. $$y=4 \sin 2 x$$

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

Sketch the curves of the given functions by addition of ordinates. $$y=x-\sin x$$

Fill in the following table for each function and plot the graph from these points. $$\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c} x & -\frac{\pi}{2} & -\frac{\pi}{3} & -\frac{\pi}{4} & -\frac{\pi}{6} & 0 & \frac{\pi}{6} & \frac{\pi}{4} & \frac{\pi}{3} & \frac{\pi}{2} & \frac{2 \pi}{3} & \frac{3 \pi}{4} & \frac{5 \pi}{6} & \pi \\ \hline y & & & & & & & & & & & & & \end{array}$$ $$y=\sec x$$

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

Fill in the following table for each finction and plot the graph from these points. $$\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c|c}x & -\frac{\pi}{2} & -\frac{\pi}{3} & -\frac{\pi}{4} & -\frac{\pi}{6} & 0 & \frac{\pi}{6} & \frac{\pi}{4} & \frac{\pi}{3} & \frac{\pi}{2} & \frac{2 \pi}{3} & \frac{3 \pi}{4} & \frac{5 \pi}{6} & \pi \\\\\hline y & & & & & & & & & & & & &\end{array}$$ $$y=\sec x$$

find the period of each function. $$y=3 \cos 8 x$$

Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the ficnctions. Check each using a calculator. $$y=\cos \left(x+\frac{\pi}{3}\right)$$

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