Chapter 5

Draw an angle in standard position. Label the vertex, initial side, and terminal side.

Explain why there are an infinite number of angles that are coterminal to a certain angle.

State what a positive or negative angle signifies, and explain how to draw each.

How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

Explain the differences between linear speed and angular speed when describing motion along a circular path.

For the following exercises, draw an angle in standard position with the given measure. $$ 30^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ 300^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -80^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ 135^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -150^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ \frac{2 \pi}{3} $$

For the following exercises, draw an angle in standard position with the given measure. $$ \frac{7 \pi}{4} $$

For the following exercises, draw an angle in standard position with the given measure. $$ \frac{5 \pi}{6} $$

For the following exercises, draw an angle in standard position with the given measure. $$ \frac{\pi}{2} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -\frac{\pi}{10} $$

For the following exercises, draw an angle in standard position with the given measure. $$ 415^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -120^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -315^{\circ} $$

For the following exercises, draw an angle in standard position with the given measure. $$ \frac{22 \pi}{3} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -\frac{\pi}{6} $$

For the following exercises, draw an angle in standard position with the given measure. $$ -\frac{4 \pi}{3} $$

For the following exercises, convert angles in radians to degrees. \(\frac{3 \pi}{4}\) radians

For the following exercises, convert angles in radians to degrees. \(\frac{\pi}{9}\) radians

For the following exercises, convert angles in radians to degrees. \(-\frac{5 \pi}{4}\) radians

For the following exercises, convert angles in radians to degrees. \(\frac{\pi}{3}\) radians

For the following exercises, convert angles in radians to degrees. \(-\frac{7 \pi}{3}\) radians

For the following exercises, convert angles in radians to degrees. \(-\frac{5 \pi}{12}\) radians

For the following exercises, convert angles in radians to degrees. \(\frac{11 \pi}{6}\) radians

For the following exercises, convert angles in degrees to radians. $$ 90^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ 100^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ -540^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ -120^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ 180^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ -315^{\circ} $$

For the following exercises, convert angles in degrees to radians. $$ 150^{\circ} $$

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 12 inches subtended by a central angle of \(\frac{\pi}{4}\) radians.

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 5.02 miles subtended by the central angle of \(\frac{\pi}{3}\) .

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of diameter 14 meters subtended by the central angle of \(\frac{5 \pi}{6}\)

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 10 centimeters subtended by the central angle of \(50^{\circ} .\)

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of radius 5 inches subtended by the central angle of \(220^{\circ} .\)

For the following exercises, use to given information to find the length of a circular arc. Round to two decimal places. Find the length of the arc of a circle of diameter 12 meters subtended by the central angle is \(63^{\circ} .\)

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle has a central angle of \(45^{\circ}\) and a radius 6 \(\mathrm{cm} .\)

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle has a central angle of \(30^{\circ}\) and a radius of 20 \(\mathrm{cm} .\)

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle with diameter 10 feet and an angle of \(\frac{\pi}{2}\) radians.

For the following exercises, use the given information to find the area of the sector. Round to four decimal places. A sector of a circle with radius of 0.7 inches and an angle of \(\pi\) radians.

For the following exercises, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal to the given angle. $$ -40^{\circ} $$

For the following exercises, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal to the given angle. $$ -110^{\circ} $$

For the following exercises, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal to the given angle. $$ 700^{\circ} $$

For the following exercises, find the angle between \(0^{\circ}\) and \(360^{\circ}\) that is coterminal to the given angle. $$ 1400^{\circ} $$

For the following exercises, find the between 0 and 2\(\pi\) in radians that is coterminal to the given angle. $$ -\frac{\pi}{9} $$