91Ó°ÊÓ

Use identities to find the exact value of each expression. Do not use a calculator. $$\sin 40^{\circ} \cos 50^{\circ}+\cos 40^{\circ} \sin 50^{\circ}$$

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\tan ^{-1}(-\sqrt{3})$$

For e expression in Column I, choose the expression from Column II that completes an identity. You may have to rewrite one or both expressions. Do not use a calculator. \(\mathbf{I}\) \(\frac{\sec x}{\csc x}=\) _______ \(\mathbf{II}\) A. \(\frac{\sin ^{2} x}{\cos ^{2} x}\) B. \(\frac{1}{\sec ^{2} x}\) C. \(\sin (-x)\) D. \(\csc ^{2} x-\cot ^{2} x+\sin ^{2} x\) E. \(\tan x\)

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\sin ^{-1} \frac{\sqrt{2}}{2}$$

Solve each equation for solutions over the interval \([0,2 \pi)\) by first solving for the trigonometric finction. Do not use a calculator. $$2 \sin x-1=\csc x$$

Use identities to find the exact value of each expression. Do not use a calculator. $$\frac{\tan 80^{\circ}+\tan 55^{\circ}}{1-\tan 80^{\circ} \tan 55^{\circ}}$$

Use an identity to write each expression as a single trigonometric function or as a single number in exact form. Do not use a calculator. $$2 \cos ^{2} 67.5^{\circ}-1$$

Solve each equation in part (a) analytically over the interval \([0,2 \pi) .\) Then use a graph to solve each inequality in part (b). (a) \(\cos x=\cos 2 x\) (b) \(\cos x<\cos 2 x\)

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\cos ^{-1}\left(-\frac{1}{2}\right)$$

Use identities to find the exact value of each expression. Do not use a calculator. $$\frac{\tan 80^{\circ}-\tan \left(-55^{\circ}\right)}{1+\tan 80^{\circ} \tan \left(-55^{\circ}\right)}$$