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

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Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).

Identify the given radian measure: \(\frac{11\pi}{6}\).

Substitute the radian value into the conversion formula: \(\frac{11\pi}{6} \times \frac{180}{\pi}\).

Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{11}{6} \times 180\).

Multiply the fraction by 180 to find the degree measure: \(11 \times \frac{180}{6}\).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.