91Ó°ÊÓ

For the following exercises, sketch the graph of each function for two full periods. Determine the amplitude, the period, and the equation for the midline. $$ f(x)=2 \csc \left(x+\frac{\pi}{4}\right)-3 $$

For the following exercises, find the amplitude, period, phase shift, and midline. $$ y=\sin \left(\frac{\pi}{6} x+\pi\right)-3 $$

For the following exercises, find the amplitude, period, phase shift, and midline. $$ y=8 \sin \left(\frac{7 \pi}{6} x+\frac{7 \pi}{2}\right)+6 $$

Water is pumped into a storage bin and empties according to a periodic rate. The depth of the water is 3 feet at its lowest at 2:00 a.m. and 71 feet at its highest, which occurs every 5 hours. Write a cosine function that models the depth of the water as a function of time, and then graph the function for one period.

For the following exercises, find the period and horizontal shift of each function. $$ g(x)=3 \tan (6 x+42) $$

For the following exercises, find the period and horizontal shift of each function. $$ n(x)=4 \csc \left(\frac{5 \pi}{3} x-\frac{20 \pi}{3}\right) $$

If \(\sec x=4,\) find \(\sec (-x)\).

For the following exercises, graph the functions on the specified window and answer the questions. Graph \(m(x)=\sin (2 x)+\cos (3 x)\) on the viewing window \([-10,10]\) by \([-3,3] .\) Approximate the graph's period.

For the following exercises, graph the functions on the specified window and answer the questions.Graph \(f(x)=\frac{\sin x}{x}\) on \([-0.5,0.5]\) and explain any observations.

For the following exercises, let \(f(x)=\frac{3}{5} \cos (6 x)\) What is the largest possible value for \(f(x) ?\)