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. $$(\cot x-\sqrt{3})(2 \sin x+\sqrt{3})=0$$

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

Solve each equation for solutions over the interval \([0,2 \pi)\) by first solving for the trigonometric finction. Do not use a calculator. $$\tan x+1=\sqrt{3}+\sqrt{3} \cot x$$

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) \(\sin \frac{x}{2}=\sqrt{2}-\sin \frac{x}{2}\) (b) \(\sin \frac{x}{2}>\sqrt{2}-\sin \frac{x}{2}\)

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. \(\mathbf{I}\) \(\sec ^{2} x-1=\) _______ \(\mathbf{II}\) 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. \(\tan x\)

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. $$1-2 \sin ^{2} 15^{\circ}$$

Use identities to find the exact value of each expression. Do not use a calculator. $$\sin 76^{\circ} \cos 31^{\circ}-\cos 76^{\circ} \sin 31^{\circ}$$

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

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) \(\sin x=\sin 2 x\) (b) \(\sin x>\sin 2 x\)

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