91Ó°ÊÓ

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

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) \(\cos 2 x=-\frac{1}{2}\) (b) \(\cos 2 x>-\frac{1}{2}\)

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\arctan (-1)$$

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

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

Use identities to find the exact value of each expression. Do not use a calculator. $$\sin \left(-15^{\circ}\right)$$

Use identities to find (a) \(\sin 2 \theta\) and (b) \(\cos 2 \theta\) $$\tan \theta=\frac{5}{3} \text { and } \sin \theta<0$$

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

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