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

Verified step by step guidance

1. Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
2. Identify the given radian measure, which is \(15\pi\) radians.
3. Substitute \(15\pi\) into the conversion formula: \(15\pi \times \frac{180}{\pi}\).
4. Simplify the expression by canceling out \(\pi\) in the numerator and denominator.
5. Multiply the remaining numbers to find the equivalent degree measure.

Key Concepts

Radian Measure

A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry and is related to degrees by the formula 180° = π radians.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the equivalence that π radians equal 180 degrees, allowing angles expressed in radians to be expressed in degrees for easier interpretation.

Simplifying Expressions Involving π

When converting angles like 15π radians, it is important to treat π as a constant and simplify the expression by multiplying the numeric coefficient by 180. This helps in obtaining the degree measure without leaving π in the final answer.