Chapter 13

Solve each equation by finding the value of \(x\) to the nearest degree. $$ x=\cos ^{-1} \frac{\sqrt{2}}{2} $$

If the given point \(P\) is located on the unit circle, find \(\sin \theta\) and \(\cos \theta\) $$ P\left(\frac{5}{13},-\frac{12}{13}\right) $$

Find the exact values of the six trigonometric functions of \(\theta\) if the terminal side of \(\theta\) in standard position contains the given point. \((-15,8)\)

Draw an angle with the given measure in standard position. \(70^{\circ}\)

Solve each equation by finding the value of \(x\) to the nearest degree. \(\operatorname{Arctan} 0=x\)

If the given point \(P\) is located on the unit circle, find \(\sin \theta\) and \(\cos \theta\) $$ P\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right) $$

Find the exact values of the six trigonometric functions of \(\theta\) if the terminal side of \(\theta\) in standard position contains the given point. \((-3,0)\)

Draw an angle with the given measure in standard position. \(300^{\circ}\)

Find the exact value of each function. $$ \sin -240^{\circ} $$

Determine whether each triangle should be solved by beginning with the Law of Sines or Law of Cosines. Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. \(A=42^{\circ}, b=57, a=63\)

Find the exact values of the six trigonometric functions of \(\theta\) if the terminal side of \(\theta\) in standard position contains the given point. \((4,4)\)

Draw an angle with the given measure in standard position. \(570^{\circ}\)

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\tan ^{-1}\left(\frac{\sqrt{3}}{3}\right)\)

Find the exact value of each function. $$ \cos \frac{10 \pi}{3} $$

Determine whether each triangle should be solved by beginning with the Law of Sines or Law of Cosines. Then solve each triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. \(a=5, b=12, c=13\)

Find the exact value of each trigonometric function. \(\sin 300^{\circ}\)

Draw an angle with the given measure in standard position. \(-45^{\circ}\)

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\cos ^{-1}(-1)\)

In Australian baseball, the bases lie at the vertices of a square 27.5 meters on a side and the pitcher’s mound is 18 meters from home plate. Find the distance from the pitcher’s mound to first base.

Find the exact value of each trigonometric function. \(\cos 180^{\circ}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(130^{\circ}\)

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\cos \left(\cos ^{-1} \frac{2}{9}\right)\)

Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle . Round measures of sides to the nearest tenth and measures of angles to the nearest degree. $$ A=123^{\circ}, a=12, b=23 $$

In Australian baseball, the bases lie at the vertices of a square 27.5 meters on a side and the pitcher’s mound is 18 meters from home plate. Find the angle between home plate, the pitcher’s mound, and first base.

Find the exact value of each trigonometric function. \(\tan \frac{5 \pi}{3}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(-10^{\circ}\)

Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle . Round measures of sides to the nearest tenth and measures of angles to the nearest degree. $$ A=30^{\circ}, a=3, b=4 $$

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\sin \left(\sin ^{-1} \frac{3}{4}\right)\)

The given point \(P\) is located on the unit circle. Find \(\sin \theta\) and \(\cos \theta\) $$ P\left(-\frac{3}{5}, \frac{4}{5}\right) $$

Find the exact value of each trigonometric function. \(\sec \frac{7 \pi}{6}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(485^{\circ}\)

Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle . Round measures of sides to the nearest tenth and measures of angles to the nearest degree. $$ A=55^{\circ}, a=10, b=5 $$

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\sin \left(\cos ^{-1} \frac{3}{4}\right)\)

The given point \(P\) is located on the unit circle. Find \(\sin \theta\) and \(\cos \theta\) $$ P\left(-\frac{12}{13},-\frac{5}{13}\right) $$

Sketch each angle. Then find its reference angle. \(235^{\circ}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(\frac{3 \pi}{4}\)

Determine whether each triangle has no solution, one solution, or two solutions. Then solve each triangle . Round measures of sides to the nearest tenth and measures of angles to the nearest degree. $$ A=145^{\circ}, a=18, b=10 $$

Find each value. Write degree measures in radians. Round to the nearest hundredth. \(\tan \left(\sin ^{-1} \frac{1}{2}\right)\)

The given point \(P\) is located on the unit circle. Find \(\sin \theta\) and \(\cos \theta\) $$ P\left(\frac{8}{17}, \frac{15}{17}\right) $$

Sketch each angle. Then find its reference angle \(\frac{7 \pi}{4}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(-\frac{\pi}{6}\)

WOODWORKING Latisha is to join a 6 -meter beam to a 7 -meter beam so the angle opposite the 7 -meter beam measures \(75^{\circ} .\) To what length should Latisha cut the third beam in order to form a triangular brace? Round to the nearest tenth.

Solve each equation by finding the value of \(x\) to the nearest degree. $$ x=\cos ^{-1} \frac{1}{2} $$

The given point \(P\) is located on the unit circle. Find \(\sin \theta\) and \(\cos \theta\) $$ P\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right) $$

Sketch each angle. Then find its reference angle. \(-240^{\circ}\)

Rewrite each degree measure in radians and each radian measure in degrees. \(\frac{19 \pi}{3}\)

Solve each equation by finding the value of \(x\) to the nearest degree. $$ \sin ^{-1} \frac{1}{2}=x $$

The given point \(P\) is located on the unit circle. Find \(\sin \theta\) and \(\cos \theta\) $$ P\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) $$

\(\cos \theta=-\frac{1}{2},\) Quadrant II

Earth rotates on its axis once every 24 hours. How long does it take Earth to rotate through an angle of \(315^{\circ} ?\)