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Chapter 4: Problem 106

Explain how to find the radian measure of a central angle.

Short Answer

Expert verified
To find the radian measure of a central angle, you need to use the conversion formula which is \( Radians = Degrees \times \frac{\pi}{180} \). Insert the degree measure into the formula to get the corresponding radian measure.

Step by step solution

01

Understanding central angles and radians

A central angle is an angle whose vertex is at the center of a circle, and its edges go through points on the circle. A radian is the standard unit measure for angles used in mathematics. It is proportional to the arc length, being the ratio between the arc length and the radius of the circle.
02

Understanding the conversion formula

The formula to convert degree measure to radian measure is given by: \( Radians = Degrees \times \frac{\pi}{180} \) where 蟺 is the constant pi (approximately equal to 3.14), and the measure in degrees is what we want to convert to radians.
03

Using the conversion formula

To find the radian measure of a central angle, we simply have to apply the given degree measure of that angle into the conversion formula. Calculate the product of the degree measure and \( \frac{\pi}{180} \) to get the radian measure.

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