91Ó°ÊÓ

Use the information given about the angle \(\theta, 0 \leq \theta<2 \pi,\) to find the exact value of: (a) \(\sin (2 \theta)\) (b) \(\cos (2 \theta)\) (c) \(\sin \frac{\theta}{2}\) (d) \(\cos \frac{\theta}{2}\) \(\sin \theta=\frac{3}{5}, \quad 0<\theta<\frac{\pi}{2}\)

True or False \(y=\tan ^{-1} x\) if and only if \(x=\tan y\) where \(-\infty

True or False The solution set of the equation \(\tan \theta=1\) is given by \(\left\\{\theta \mid \theta=\frac{\pi}{4}+k \pi, k\right.\) an integer \(\\}\).

Multiple Choice \(\sin ^{-1}(\sin x)=x\) for all numbers \(x\) for which (a) \(-\infty

The expression \(\frac{1}{1-\sin \theta}+\frac{1}{1+\sin \theta}\) simplifies to which of the following? (a) \(2 \cos ^{2} \theta\) (b) \(2 \sec ^{2} \theta\) (c) \(2 \sin ^{2} \theta\) (d) \(2 \csc ^{2} \theta\)

Use the information given about the angle \(\theta, 0 \leq \theta<2 \pi,\) to find the exact value of: (a) \(\sin (2 \theta)\) (b) \(\cos (2 \theta)\) (c) \(\sin \frac{\theta}{2}\) (d) \(\cos \frac{\theta}{2}\) \(\cos \theta=\frac{3}{5}, \quad 0<\theta<\frac{\pi}{7}\)

Express each product as a sum containing only sines or only cosines $$ \sin (3 \theta) \sin (5 \theta) $$

Find the exact value of each expression. $$ \cot ^{-1} 1 $$

True or False The equation \(\sin \theta=2\) has a real solution that can be found using a calculator.

In Problems 11-26, find the exact value of each expression. \(\sin ^{-1} 0\)