Chapter 16

Simplify. $$2 \sin ^{2} x+\cos 2 x$$

Evaluate each trigonometric expression to three significant digits. $$5.27 \sin 45.8^{\circ}-1.73$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$\sin x=\frac{1}{2}$$

Expand by means of the addition and subtraction formulas, and simplify. $$\sin \left(\theta+30^{\circ}\right)$$

Evaluate each trigonometric expression to three significant digits. $$2.84 \cos 73.4^{\circ}-3.83 \tan 36.2^{\circ}$$

Simplify. $$2 \sin 2 \theta \cos 2 \theta$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$2 \cos x-\sqrt{3}=0$$

Expand by means of the addition and subtraction formulas, and simplify. $$\cos \left(45^{\circ}-x\right)$$

Change to an expression containing only sin and cos. $$\cot x+\csc x$$

Simplify. $$\frac{2 \tan x}{1+\tan ^{2} x}$$

Evaluate each trigonometric expression to three significant digits. $$3.72\left(\sin 28.3^{\circ}+\cos 72.3^{\circ}\right)$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$1-\tan x=0$$

Expand by means of the addition and subtraction formulas, and simplify. $$\sin \left(x+60^{\circ}\right)$$

Change to an expression containing only sin and cos. $$\tan \theta \csc \theta$$

Simplify. $$\frac{2-\sec ^{2} x}{\sec ^{2} x}$$

Expand by means of the addition and subtraction formulas, and simplify. $$\tan (\pi+\theta)$$

Change to an expression containing only sin and cos. $$\sec \theta-\tan \theta \sin \theta$$

Prove each identity. $$\frac{2 \tan \theta}{1-\tan ^{2} \theta}=\tan 2 \theta$$

Evaluate each trigonometric expression to three significant digits. $$2.84(5.28 \cos 2-2.82)+3.35$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$4 \sin ^{2} x=3$$

Expand by means of the addition and subtraction formulas, and simplify. $$\cos \left(x+\frac{\pi}{2}\right)$$

Change to an expression containing only sin and cos. $$\frac{\tan \theta}{\csc \theta}+\frac{\sin \theta}{\tan \theta}$$

Prove each identity. $$\frac{1-\tan ^{2} x}{1+\tan ^{2} x}=\cos 2 x$$

Evaluate each trigonometric expression to three significant digits. $$2.63 \sin 2.4+1.36 \cos 3.5+3.13 \tan 2.5$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$2 \sin 3 x=\frac{1}{2}$$

Change to an expression containing only sin and cos. $$\cot x+\tan x$$

Evaluate each trigonometric expression to three significant digits. $$\sin 35^{\circ}+\cos 35^{\circ}$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$3 \sin x-1=2 \sin x$$

Expand by means of the addition and subtraction formulas, and simplify. $$\sin (\theta+2 \phi)$$

Evaluate each trigonometric expression to three significant digits. $$\sin 125^{\circ} \tan 225^{\circ}$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$\csc ^{2} x=4$$

Simplify. $$\frac{\csc \theta}{\sin \theta}$$

Evaluate each trigonometric expression to three significant digits. $$\cos 270^{\circ} \cos 150^{\circ}+\sin 270^{\circ} \sin 150^{\circ}$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$2 \cos ^{2} x=1+2 \sin ^{2} x$$

Simplify. $$\cos 2 x \cos 9 x+\sin 2 x \sin 9 x$$

Simplify. $$\frac{\cos \theta}{\cot \theta}$$

Prove each identity. $$\frac{\sin 2 \theta+\sin \theta}{1+\cos \theta+\cos 2 \theta}=\tan \theta$$

Evaluate each trigonometric expression to three significant digits. $$\frac{\sin ^{2} 155^{\circ}}{1+\cos 155^{\circ}}$$

Simplify. $$\sin \theta \csc \theta$$

Evaluate each trigonometric expression to three significant digits. $$\sin ^{2} 75^{\circ}$$

Simplify. $$\sin 3 \theta \cos 2 \theta-\cos 3 \theta \sin 2 \theta$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$4 \sin ^{4} x=1$$

Simplify. $$\tan \theta \csc \theta$$

Prove each identity. $$\frac{\sin 2 \alpha+1}{\cos \alpha+\sin \alpha}=\sin \alpha+\cos \alpha$$

Evaluate each trigonometric expression to three significant digits. $$\tan ^{2} 125^{\circ}-\cos ^{2} 125^{\circ}$$

Prove each identity. $$\cos x=\sin \left(x+90^{\circ}\right)$$

Simplify. $$\frac{\sin \theta}{\csc \theta}$$

Evaluate each trigonometric expression to three significant digits. $$\left(\cos ^{2} 206^{\circ}+\sin 206^{\circ}\right)^{2}$$

Prove each identity. $$\sin (\alpha+\beta)+\sin (\alpha-\beta)=2 \sin \alpha \cos \beta$$

Solve each equation for all nonnegative values of \(x\) less than \(360^{\circ} .\) Do some by calculator. $$1+\tan x=\sec ^{2} x$$