91Ó°ÊÓ

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

Use the even-odd identities to write of the following expressions as a trigonometric function of a positive number $$\cot \left(-\frac{4 \pi}{7}\right)$$

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\sin ^{-1} 0$$

How many solutions does \(\sin x=\frac{1}{2}\) have on \([0,2 \pi) ?\) How many solutions does \(\sin 2 x=\frac{1}{2}\) have on \([0,2 \pi)\) ? Explain how a graph supports your answer.

Use identities to find (a) \(\sin 2 \theta\) and (b) \(\cos 2 \theta\) $$\cos \theta=-\frac{12}{13} \text { and } \sin \theta>0$$

Use identities to find the exact value of each expression. Do not use a calculator. $$\sin 105^{\circ}$$

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

For expression in Column I, choose the expression from Column II that completes a fundamental identity. Do not use a calculator. \(\mathbf{I}\) \(\frac{\cos x}{\sin x}=\)_______ \(\mathbf{II}\) A. \(\sin ^{2} x+\cos ^{2} x\) B. cot \(x\) C. \(\sec ^{2} x\) D. \(\frac{\sin x}{\cos x}\) E. \(\cos x\)

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) \(\cos 2 x=\frac{\sqrt{3}}{2}\) (b) \(\cos 2 x>\frac{\sqrt{3}}{2}\)

Use identities to find the exact value of each expression. Do not use a calculator. $$\tan 105^{\circ}$$