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

Verified step by step guidance

1. Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
2. Substitute the given radian measure \(\frac{11\pi}{15}\) into the formula: \(\text{Degrees} = \frac{11\pi}{15} \times \frac{180}{\pi}\).
3. Simplify the expression by canceling out \(\pi\) in the numerator and denominator: \(\text{Degrees} = \frac{11}{15} \times 180\).
4. Multiply the fraction \(\frac{11}{15}\) by 180 to find the degree measure: \(\text{Degrees} = 11 \times \frac{180}{15}\).
5. Simplify the multiplication and division to express the angle in degrees.

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, where 2π radians equal 360 degrees.

Degree Measure

Degrees are another unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and are related to radians by the conversion factor 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 of π radians to 180 degrees, allowing you to express angles in the more familiar degree unit.