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1. Measuring Angles

Radians

1. Measuring Angles

Radians

Guided videos.

Learn with Patrick

Go to the course

Converting between Degrees & Radians

Converting between Degrees & Radians

Additional 5 creators.

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What is the radian measure of an angle

What is the radian measure of an angle

Introduction to radians | Unit circle definition of trig functions

Introduction to radians | Unit circle definition of trig functions

Intro to Radians

Intro to Radians

What are Radians? | Radian (Unit of Plane Angle)

What are Radians? | Radian (Unit of Plane Angle)

Introduction to Radians - Comparing measurement systems

Introduction to Radians - Comparing measurement systems

Introduction to Trigonometry: Angles and Radians

Introduction to Trigonometry: Angles and Radians

Professor Dave Explains

Radians and Degrees

Radians and Degrees

Radian and degree conversion practice

Radian and degree conversion practice

Converting Degrees to Radians

Converting Degrees to Radians

Mario's Math Tutoring

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Practice this topic

Multiple Choice

Convert the angle $540°$ from degrees to radians.

Multiple Choice

Convert the angle $-\frac{5\pi}{6}$ from radians to degrees.

Textbook Question

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

Textbook Question

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

Textbook Question

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°

Textbook Question

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°

Textbook Question

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°

Textbook Question

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°

Textbook Question

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

Textbook Question

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.

Textbook Question

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.

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

Convert 135° to an exact radian measure.

Textbook Question

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

Textbook Question

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

Textbook Question

CONCEPT PREVIEW Find the radius of each circle.

Textbook Question

CONCEPT PREVIEW Find the radius of each circle.

Textbook Question

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

Textbook Question

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

Textbook Question

CONCEPT PREVIEW Find the area of each sector.

Textbook Question

CONCEPT PREVIEW Find the area of each sector.

Textbook Question

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

Textbook Question

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

Textbook Question

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°

Textbook Question

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°

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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°

Textbook Question

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°

Textbook Question

Work each problem. See Example 5. Angle Measure Find the measure (in radians) of a central angle of a sector of area 16 in² a circle of radius 3.0 in.

Textbook Question

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.

Textbook Question

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?

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

Textbook Question

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

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