1. Measuring Angles

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

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

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

What is the radian equivalent of $180°$?

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

What is $270°$ converted to 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 = 29.2 m, θ = 5π/6 radians

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

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

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

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

-4.8 radians

When a particle completes one full revolution in circular motion, how many radians of angle does it cover?

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

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