1. Measuring Angles

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ ―1800°

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ ―8π/5

In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 12 inches Central Angle, θ: θ = 45°

In Exercises 71–74, find the length of the arc on a circle of radius r intercepted by a central angle θ. Express arc length in terms of 𝜋. Then round your answer to two decimal places. Radius, r: 8 feet Central Angle, θ: θ = 225°

In Exercises 75–78, find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 10 meters Central Angle, θ: θ = 18°

In Exercises 75–78, find the area of the sector of a circle of radius r formed by a central angle θ. Express area in terms of π. Then round your answer to two decimal places. Radius, r: 4 inches Central Angle, θ: θ = 240°

In Exercises 91–92, find the measure of the central angle on a circle of radius r that forms a sector with the given area. Radius, r: 10 feet Area of the Sector, A: 25 square feet

Find the length of the arc on a circle of radius 10 feet intercepted by a 135° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

Find the length of the arc on a circle of radius 20 feet intercepted by a 75° central angle. Express arc length in terms of 𝜋. Then round your answer to two decimal places.

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 10 inches Arc Length, s: 40 inches

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 6 yards Arc Length, s: 8 yards

In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 1 meter Arc Length, s: 600 centimeters

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 18°

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 150°

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 330°

In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. -270°

In Exercises 21–28, convert each angle in radians to degrees. 𝜋 2

In Exercises 21–28, convert each angle in radians to degrees. 2𝜋 3

In Exercises 21–28, convert each angle in radians to degrees. 7𝜋 6

In Exercises 21–28, convert each angle in radians to degrees. -3𝜋

In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. 18°

In Exercises 29–34, convert each angle in degrees to radians. Round to two decimal places. -50°

In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. 2 radians

In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. 𝜋/13 radians

In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. -4.8 radians

In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. -5.2 radians

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 15°

In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 315°

In Exercises 5–7, convert each angle in radians to degrees. 5𝜋 3

In Exercises 5–7, convert each angle in radians to degrees. 7𝜋 5

In Exercises 5–7, convert each angle in radians to degrees. - 5𝜋 6

Convert 135° to an exact radian measure.

CONCEPT PREVIEW Find the exact length of each arc intercepted by the given central angle. ​​

CONCEPT PREVIEW Find the exact length of each arc intercepted by the given central angle. ​​

CONCEPT PREVIEW Find the radius of each circle.

CONCEPT PREVIEW Find the radius of each circle.

CONCEPT PREVIEW Find the measure of each central angle (in radians).

CONCEPT PREVIEW Find the measure of each central angle (in radians).

CONCEPT PREVIEW Find the area of each sector.

CONCEPT PREVIEW Find the area of each sector.

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 12.3 cm , θ = 2π/3 radians

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 1.38 ft , θ = 5π/6 radians

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 4.82 m , θ = 60°

Find the length to three significant digits of each arc intercepted by a central angle in a circle of radius r. See Example 1. r = 15.1 in. , θ = 210°

Concept Check If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed?

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Panama City, Panama, 9° N, and Pittsburgh, Pennsylvania, 40° N

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Farmersville, California, 36° N, and Penticton, British Columbia, 49° N

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. New York City, New York, 41° N, and Lima, Peru, 12° S

Distance between Cities Find the distance in kilometers between each pair of cities, assuming they lie on the same north-south line. Assume the radius of Earth is 6400 km. See Example 2. Halifax, Nova Scotia , 45° N, and Buenos Aires, Argentina, 34° S

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . ​​30 min

Distance Traveled by a Minute Hand Suppose the tip of the minute hand of a clock is 3 in. from the center of the clock. For each duration, determine the distance traveled by the tip of the minute hand. Leave answers as multiples of π . 4.5 hr

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 29.2 m, θ = 5π/6 radians

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 30.0 ft, θ = π/2 radians

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 12.7 cm, θ = 81°

Find the area of a sector of a circle having radius r and central angle θ. Express answers to the nearest tenth. See Example 5. r = 40.0 mi, θ = 135°

Work each problem. See Example 5. A​​​​ngle Measure Find t​​he measure (in radians) of a central angle of a sector of area 16 in² a circle of radius 3.0 in.

Work each problem. See Example 5. Irrigation Area A center-pivot irrigation system provides water to a sector-shaped field as shown in the figure. Find the area of the field if θ = 40.0° and r = 152 yd.

Work each problem. See Example 5. Arc Length A circular sector has an area of 50 in² . The radius of the circle is 5 in. What is the arc length of the sector?

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 30°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 90°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 150°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ ―300°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ ―315°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 450°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 1800°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 3600°

Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ ―900°

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ π/3

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ 7π/4

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ 11π/6

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ 11π/15

Convert each radian measure to degrees. See Examples 2(a) and 2(b). ​​ ―π/6