Chapter 6

Sketch each triangle, and then solve the triangle using the Law of sines. $$\angle A=22^{\circ}, \quad \angle B=95^{\circ}, \quad a=420$$

Find the degree measure of the angle with the given radian measure. $$\frac{11 \pi}{3}$$

Solve triangle \(A B C\). \(b=125, \quad c=162, \quad \angle B=40^{\circ}\)

Find the exact value of the trigonometric function. $$\csc \left(-630^{\circ}\right)$$

Sketch each triangle, and then solve the triangle using the Law of sines. $$\angle B=29^{\circ}, \quad \angle C=51^{\circ}, \quad b=44$$

Find the degree measure of the angle with the given radian measure. $$-\frac{5 \pi}{4}$$

Solve triangle \(A B C\). \(a=65, \quad c=50, \quad \angle C=52^{\circ}\)

Find the exact value of the trigonometric function. $$\cot 210^{\circ}$$

Sketch each triangle, and then solve the triangle using the Law of sines. $$\angle B=10^{\circ}, \quad \angle C=100^{\circ}, \quad c=115$$

Find the degree measure of the angle with the given radian measure. $$-\frac{3 \pi}{2}$$

Solve triangle \(A B C\). \(a=50, \quad b=65, \quad \angle A=55^{\circ}\)

Find the exact value of the trigonometric function. $$\cos 570^{\circ}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=28, \quad b=15, \quad \angle A=110^{\circ}$$

Sketch a triangle that has acute angle \(\theta\), and find the other five trigonometric ratios of \(\theta\). $$\sin \theta=\frac{3}{5}$$

Find the degree measure of the angle with the given radian measure. $$3$$

Solve triangle \(A B C\). \(a=73.5, \quad \angle B=61^{\circ}, \quad \angle C=83^{\circ}\)

Find the exact value of the trigonometric function. $$\sec 120^{\circ}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=30, \quad c=40, \quad \angle A=37^{\circ}$$

Find the degree measure of the angle with the given radian measure. $$-2$$

Find the exact value of the trigonometric function. $$\tan 750^{\circ}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\sin \theta=\frac{1}{2}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=20, \quad c=45, \quad \angle A=125^{\circ}$$

Sketch a triangle that has acute angle \(\theta\), and find the other five trigonometric ratios of \(\theta\). $$\cot \theta=1$$

Find the degree measure of the angle with the given radian measure. $$-1.2$$

Find the exact value of the trigonometric function. $$\cos 660^{\circ}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\sin \theta=\frac{\sqrt{3}}{2}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$b=45, \quad c=42, \quad \angle C=38^{\circ}$$

Sketch a triangle that has acute angle \(\theta\), and find the other five trigonometric ratios of \(\theta\). $$\tan \theta=\sqrt{3}$$

Find the degree measure of the angle with the given radian measure. $$3.4$$

Find the exact value of the trigonometric function. $$\sin \frac{2 \pi}{3}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\sin \theta=0.7$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$b=25, \quad c=30, \quad \angle B=25^{\circ}$$

Sketch a triangle that has acute angle \(\theta\), and find the other five trigonometric ratios of \(\theta\). $$\sec \theta=\frac{7}{2}$$

Find the degree measure of the angle with the given radian measure. $$\frac{\pi}{10}$$

Find the exact value of the trigonometric function. $$\sin \frac{5 \pi}{3}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\sin \theta=\frac{1}{4}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=75, \quad b=100, \quad \angle A=30^{\circ}$$

Sketch a triangle that has acute angle \(\theta\), and find the other five trigonometric ratios of \(\theta\). $$\csc \theta=\frac{13}{12}$$

Find the degree measure of the angle with the given radian measure. $$\frac{5 \pi}{18}$$

Find the exact value of the trigonometric function. $$\sin \frac{3 \pi}{2}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\cos \theta=0.7$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=50, \quad b=100, \quad \angle A=50^{\circ}$$

Evaluate the expression without using a calculator. $$\sin \frac{\pi}{6}+\cos \frac{\pi}{6}$$

Find the degree measure of the angle with the given radian measure. $$-\frac{2 \pi}{15}$$

Find the exact value of the trigonometric function. $$\cos \frac{7 \pi}{3}$$

Find all angles \(\theta\) between \(0^{\circ}\) and \(180^{\circ}\) satisfying the given equation. $$\cos \theta=\frac{1}{9}$$

Use the Law of sines to solve for all possible triangles that satisfy the given conditions. $$a=100, \quad b=80, \quad \angle A=135^{\circ}$$

Evaluate the expression without using a calculator. $$\sin 30^{\circ} \csc 30^{\circ}$$

Find the degree measure of the angle with the given radian measure. $$-\frac{13 \pi}{12}$$

Find the exact value of the trigonometric function. $$\cos \left(-\frac{7 \pi}{3}\right)$$