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) \(\cos \frac{\theta}{2}\) \(\cot \theta=-2, \quad \sec \theta<0\)

Find the exact value of each expression. \(\sin ^{-1} \frac{\sqrt{2}}{2}\)

Simplify each trigonometric expression by following the indicated direction. Multiply and simplify: \(\frac{(\sin \theta+\cos \theta)(\sin \theta+\cos \theta)-1}{\sin \theta \cos \theta}\)

Express each sum or difference as a product of sines and/or cosines. $$ \sin (4 \theta)-\sin (2 \theta) $$

Find the exact value of each expression. \(\tan ^{-1} \frac{\sqrt{3}}{3}\)

Simplify each trigonometric expression by following the indicated direction. Multiply and simplify: \(\frac{(\tan \theta+1)(\tan \theta+1)-\sec ^{2} \theta}{\tan \theta}\)

Express each sum or difference as a product of sines and/or cosines. $$ \sin (4 \theta)+\sin (2 \theta) $$

Solve each equation on the interval \(4 \sec \theta+6=-2\)

Simplify each trigonometric expression by following the indicated direction. Factor and simplify: \(\frac{3 \sin ^{2} \theta+4 \sin \theta+1}{\sin ^{2} \theta+2 \sin \theta+1}\)

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) \(\cos \frac{\theta}{2}\) \(\cot \theta=3, \quad \cos \theta<0\)