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

Verified step by step guidance

1. Understand the relationship between radians and degrees: 1 radian is equal to \( \frac{180}{\pi} \) degrees.
2. To convert radians to degrees, multiply the radian measure by \( \frac{180}{\pi} \).
3. Apply the conversion formula to the given radian measure: \( 15\pi \times \frac{180}{\pi} \).
4. Simplify the expression by canceling out \( \pi \) from the numerator and the denominator.
5. Multiply the remaining numbers to find the degree measure.

Key Concepts

Radian Measure

A radian is a unit of angular measure used in mathematics. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. One complete revolution around a circle corresponds to 2π radians, making it a fundamental concept in trigonometry for measuring angles.

Degree Measure

Degrees are another unit of angular measurement, where one complete revolution is divided into 360 equal parts. Each degree can be further divided into 60 minutes, and each minute into 60 seconds. The conversion between radians and degrees is essential for solving problems in trigonometry, especially when interpreting angles in different contexts.

Conversion Formula

To convert radians to degrees, the formula used is: degrees = radians × (180/π). This relationship allows for the easy transformation of angle measures from one unit to another, facilitating calculations and comparisons in trigonometric functions and applications.