91Ó°ÊÓ

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

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

For expression in Column I, choose the expression from Column II that completes a fundamental identity. Do not use a calculator. \(\mathbf{I}\) \(\cos (-x)=\) _______ \(\mathbf{II}\) 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 for solutions over the interval \([0,2 \pi)\) by first solving for the trigonometric finction. Do not use a calculator. $$\cos ^{2} x+2 \cos x+1=0$$

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

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) \(\sin 3 x=0\) (b) \(\sin 3 x<0\)

Use identities to find the exact value of each expression. Do not use a calculator. $$\tan \left(-75^{\circ}\right)$$

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

For expression in Column I, choose the expression from Column II that completes a fundamental identity. Do not use a calculator. \(\mathbf{I}\) \(\tan ^{2} x+1=\) _______ \(\mathbf{II}\) A. \(\sin ^{2} x+\cos ^{2} x\) B. cot \(x\) C. \(\sec ^{2} x\) D. \(\frac{\sin x}{\cos x}\) E. \(\cos x\)

Find the exact value of each real number \(y .\) Do not use a calculator. $$y=\arctan 0$$