Convert each radian measure to degrees.

5π/4

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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: \(\frac{5\pi}{4}\).

Substitute the radian value into the conversion formula: \(\frac{5\pi}{4} \times \frac{180}{\pi}\).

Simplify the expression by canceling out \(\pi\) in the numerator and denominator: \(\frac{5}{4} \times 180\).

Multiply the remaining numbers to find the degree measure: \(5 \times \frac{180}{4}\).

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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 conversion factor 180° = π radians.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and can be converted to radians using the relationship 1 radian = 180/π degrees.

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.

Convert each radian measure to degrees.5π/4