91Ó°ÊÓ

Use a graphing calculator to plot \(Y_{1}=\sin \left(\sin ^{-1} x\right)\) and \(Y_{2}=x\) for the domain \(-1 \leq x \leq 1 .\) If you then increase the domain to \(-3 \leq x \leq 3,\) you get a different result. Explain the result.

Solve \(16 \sin ^{4} \theta-8 \sin ^{2} \theta=-1\) over \(0 \leq \theta \leq 2 \pi\).

Determine whether each statement is true or false. $$\sin (2 A)+\sin (2 A)=\sin (4 A)$$

Solve \(\left|\cos \left(\theta+\frac{\pi}{4}\right)\right|=\frac{\sqrt{3}}{2}\) over all real numbers.

Determine whether each statement is true or false. $$\cos (4 A)-\cos (2 A)=\cos (2 A)$$

Use a graphing calculator to plot \(Y_{1}=\cos \left(\cos ^{-1} x\right)\) and \(Y_{2}=x\) for the domain \(-1 \leq x \leq 1 .\) If you then increase the domain to \(-3 \leq x \leq 3,\) you get a different result. Explain the result.

Use a graphing calculator to plot \(Y_{1}=\csc ^{-1}(\csc x)\) and \(Y_{2}=x .\) Determine the domain for which the following statement is true: \(\csc ^{-1}(\csc x)=x .\) Give the domain in terms of \(\pi\).

Determine whether each statement is true or false. $$\text { If } \tan x>0, \text { then } \tan (2 x)>0$$

Solve for the smallest positive \(x\) that makes this statement true: $$\sin \left(x+\frac{\pi}{4}\right)+\sin \left(x-\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}$$

Use a graphing calculator to plot \(Y_{1}=\sec ^{-1}(\sec x)\) and \(Y_{2}=x .\) Determine the domain for which the following statement is true: \(\sec ^{-1}(\sec x)=x .\) Give the domain in terms of \(\pi\).