Chapter 6

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle A=22^{\circ}, \quad \angle B=95^{\circ}, \quad a=420 $$

Find the exact value of the trigonometric function. $$ \sec 300^{\circ} $$

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

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

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle B=29^{\circ}, \quad \angle C=51^{\circ}, \quad b=44 $$

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

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

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

13-18 $$ Sketch each triangle, and then solve the triangle using the Law of Sines. $$ \angle B=10^{\circ}, \quad \angle C=100^{\circ}, \quad c=115 $$

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

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ a=28, \quad b=15, \quad \angle A=110^{\circ} $$

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

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

\(19-28\) . 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 exact value of the trigonometric function. $$ \sec 120^{\circ} $$

Sketch a triangle that has acute angle \(\theta,\) and find the other five trigonometric ratios of \(\theta\) . $$ \cos \theta=\frac{9}{40} $$

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ a=20, \quad c=45, \quad \angle A=125^{\circ} $$

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ b=45, \quad c=42, \quad \angle C=38^{\circ} $$

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ b=25, \quad c=30, \quad \angle B=25^{\circ} $$

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ a=75, \quad b=100, \quad \angle A=30^{\circ} $$

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

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

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

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

\(19-28\) . Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. $$ a=100, \quad b=80, \quad \angle A=135^{\circ} $$

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

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. \(-\frac{13 \pi}{12}\)