Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/6

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: \(\frac{11\pi}{6}\).
3. Substitute the radian value into the conversion formula: \(\frac{11\pi}{6} \times \frac{180}{\pi}\).
4. Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{11}{6} \times 180\).
5. Multiply the fraction by 180 to find the degree measure: \(11 \times \frac{180}{6}\).

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 a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree can be further divided into minutes and seconds, but for most trigonometry problems, degrees are used as a straightforward measure of angle size.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This ratio comes from the equivalence of 2π radians to 360 degrees. For example, 11π/6 radians equals (11π/6) × (180/π) = 330 degrees.