Convert each radian measure to degrees. See Examples 2(a) and 2(b). π/3

검증된 단계별 안내

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

Identify the given radian measure, which is \(\frac{\pi}{3}\).

Substitute the radian value into the conversion formula: \(\frac{\pi}{3} \times \frac{180}{\pi}\).

Simplify the expression by canceling out \(\pi\) in the numerator and denominator.

Calculate the remaining fraction \(\frac{180}{3}\) to find the degree measure.

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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 and is related to degrees by the formula 2π radians = 360 degrees.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation. Degrees are often used in practical applications and are convertible to radians using a fixed ratio.

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, π/3 radians equals (π/3) × (180/π) = 60 degrees.