Chapter 8

\(3-16 \cdot\) Solve the given equation. $$ \tan \theta+1=\sec \theta $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \sin 18^{\circ} \cos 27^{\circ}+\cos 18^{\circ} \sin 27^{\circ} $$

Simplify the trigonometric expression. $$ \frac{1+\cos y}{1+\sec y} $$

\(3-16 \cdot\) Solve the given equation. $$ 2 \tan \theta+\sec ^{2} \theta=4 $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \cos 10^{\circ} \cos 80^{\circ}-\sin 10^{\circ} \sin 80^{\circ} $$

Simplify the trigonometric expression. $$ \frac{\tan x}{\sec (-x)} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 2 \cos 3 \theta=1 $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \cos \frac{3 \pi}{7} \cos \frac{2 \pi}{21}+\sin \frac{3 \pi}{7} \sin \frac{2 \pi}{21} $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \cos \theta=-\frac{\sqrt{3}}{2} $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \sin 15^{\circ} $$

Simplify the trigonometric expression. $$ \frac{\sec ^{2} x-1}{\sec ^{2} x} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 3 \csc ^{2} \theta=4 $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \cos \theta=\frac{1}{2} $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \frac{\tan \frac{\pi}{18}+\tan \frac{\pi}{9}}{1-\tan \frac{\pi}{18} \tan \frac{\pi}{9}} $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \tan 15^{\circ} $$

Simplify the trigonometric expression. $$ \frac{\sec x-\cos x}{\tan x} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 2 \cos 2 \theta+1=0 $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \sin \theta=\frac{\sqrt{2}}{2} $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \frac{\tan 73^{\circ}-\tan 13^{\circ}}{1+\tan 73^{\circ} \tan 13^{\circ}} $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \tan 22.5^{\circ} $$

Simplify the trigonometric expression. $$ \frac{1+\csc x}{\cos x+\cot x} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 2 \sin 3 \theta+1=0 $$

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$ \cos \frac{13 \pi}{15} \cos \left(-\frac{\pi}{5}\right)-\sin \frac{13 \pi}{15} \sin \left(-\frac{\pi}{5}\right) $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \sin 75^{\circ} $$

Simplify the trigonometric expression. $$ \frac{\sin x}{\csc x}+\frac{\cos x}{\sec x} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \sqrt{3} \tan 3 \theta+1=0 $$

Prove the cofunction identity using the Addition and Subtraction Formulas. $$ \tan \left(\frac{\pi}{2}-u\right)=\cot u $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \cos \theta=0.28 $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \cos 165^{\circ} $$

Simplify the trigonometric expression. $$ \frac{1+\sin u}{\cos u}+\frac{\cos u}{1+\sin u} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \sec 4 \theta-2=0 $$

Prove the cofunction identity using the Addition and Subtraction Formulas. $$ \cot \left(\frac{\pi}{2}-u\right)=\tan u $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \tan \theta=2.5 $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \cos 112.5^{\circ} $$

Simplify the trigonometric expression. $$ \tan x \cos x \csc x $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \cos \frac{\theta}{2}-1=0 $$

Prove the cofunction identity using the Addition and Subtraction Formulas. $$ \sec \left(\frac{\pi}{2}-u\right)=\csc u $$

\(17-24\) n Solve the given equation, and list six specific solutions. $$ \tan \theta=-10 $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \tan \frac{\pi}{8} $$

Simplify the trigonometric expression. $$ \frac{2+\tan ^{2} x}{\sec ^{2} x}-1 $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \tan \frac{\theta}{4}+\sqrt{3}=0 $$

Prove the cofunction identity using the Addition and Subtraction Formulas. $$ \csc \left(\frac{\pi}{2}-u\right)=\sec u $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \cos \frac{3 \pi}{8} $$

Simplify the trigonometric expression. $$ \frac{1+\cot A}{\csc A} $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ 2 \sin \frac{\theta}{3}+\sqrt{3}=0 $$

Prove the identity. $$ \sin \left(x-\frac{\pi}{2}\right)=-\cos x $$

\(25-38\) . Find all solutions of the given equation. $$ \cos \theta+1=0 $$

\(17-28\) Use an appropriate Half-Angle Formula to find the exact value of the expression. $$ \cos \frac{\pi}{12} $$

Simplify the trigonometric expression. $$ \tan \theta+\cos (-\theta)+\tan (-\theta) $$

\(17-34\) . An equation is given. (a) Find all solutions of the equation. (b) Find the solutions in the interval \([0,2 \pi) .\) $$ \sec \frac{\theta}{2}=\cos \frac{\theta}{2} $$