91Ó°ÊÓ

Is the graph of \(y=\sin \left(2 x-\frac{\pi}{4}\right)\) the graph of \(y=\sin 2 x\) moved \(\frac{\pi}{4}\) units to the right? Explain why or why not.

In the interval \(0 \leq x \leq \pi,\) cos \(x\) decreases. Describe the change in sec \(x\) in the same interval.

Is the graph of \(y=\cos x\) its own image under the translation \(T_{-2 \pi, 0} ?\) Justify your answer.

Does \(y=\tan x\) have a maximum and a minimum value? Justify your answer.

Is the graph of \(y=\sin 2(x+\pi)\) the same as the graph of \(y=\sin 2 x ?\) Explain why or why not.

Sketch the graph of \(y=\sin x\) in the interval \(0 \leq x \leq 4 \pi\) a. In the interval \(0 \leq x \leq 4 \pi,\) for what values of \(x\) is the graph of \(y=\sin x\) increasing? b. In the interval \(0 \leq x \leq 4 \pi\) , for what values of \(x\) is the graph of \(y=\sin x\) decreasing? c. How many cycles of the graph of \(y=\sin x\) are in the interval \(0 \leq x \leq 4 \pi ?\)

Sketch the graph of \(y=\tan x\) from \(x=-\frac{3 \pi}{2}\) to \(x=\frac{3 \pi}{2}\) a. What is the period of \(y=\tan x ?\) b. What is the domain of \(y=\tan x ?\) c. What is the range of \(y=\tan x ?\)

In \(3-14,\) sketch one cycle of the graph. $$ y=2 \sin x $$

Sketch the graph of \(y=\cos x\) in the interval \(0 \leq x \leq 4 \pi\) a. In the interval \(0 \leq x \leq 4 \pi,\) for what values of \(x\) is the graph of \(y=\cos x\) increasing? b. In the interval \(0 \leq x \leq 4 \pi,\) for what values of \(x\) is the graph of \(y=\cos x\) decreasing? c. How many cycles of the graph of \(y=\cos x\) are in the interval \(0 \leq x \leq 4 \pi ?\)

Find the amplitude of each function. \(y=\sin x\)