91Ó°ÊÓ

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

If all solutions of a trigonometric equation are given by the general formula \(\theta=\frac{\pi}{6}+2 k \pi\) or \(\theta=\frac{11 \pi}{6}+2 k \pi,\) where \(k\) is an integer, then which of the following is not a solution of the equation? (a) \(\frac{35 \pi}{6}\) (b) \(\frac{23 \pi}{6}\) (c) \(\frac{13 \pi}{6}\) (d) \(\frac{7 \pi}{6}\)

Simplify each trigonometric expression by following the indicated direction. Rewrite in terms of sine and cosine functions: $$\tan \theta \cdot \csc \theta$$

Find the exact value of each expression. $$ \csc ^{-1}(-1) $$

Multiple Choice Choose the expression that completes the Sum Formula for tangent functions: \(\tan (\alpha+\beta)=\) _____. (a) \(\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta}\) (b) \(\frac{\tan \alpha-\tan \beta}{1+\tan \alpha \tan \beta}\) (c) \(\frac{\tan \alpha+\tan \beta}{1+\tan \alpha \tan \beta}\) (d) \(\frac{\tan \alpha-\tan \beta}{1-\tan \alpha \tan \beta}\)

Suppose \(\theta=\frac{\pi}{2}\) is the only solution of a trigonometric equation in the interval \(0 \leq \theta<2 \pi\) Assuming a period of \(2 \pi,\) which of the following formulas gives all solutions of the equation, where \(k\) is an integer? (a) \(\theta=\frac{\pi}{2}+2 k \pi\) (b) \(\theta=\frac{\pi}{2}+k \pi\) (c) \(\theta=\frac{k \pi}{2}\) (d) \(\theta=\frac{\pi+k \pi}{2}\)

Express each product as a sum containing only sines or only cosines $$ \sin (4 \theta) \cos (6 \theta) $$

Simplify each trigonometric expression by following the indicated direction. $$\cot \theta \cdot \sec \theta$$

Multiple Choice Choose the expression that is equivalent to $$ \sin 60^{\circ} \cos 20^{\circ}+\cos 60^{\circ} \sin 20^{\circ} $$ (a) \(\cos 40^{\circ}\) (b) \(\sin 40^{\circ}\) (c) \(\cos 80^{\circ}\) (d) \(\sin 80^{\circ}\)

Find the exact value of each expression. \(\cos ^{-1} 1\)