Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―8π/5

검증된 단계별 안내

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

Identify the given radian measure: \(-\frac{8\pi}{5}\).

Substitute the radian value into the conversion formula: \(-\frac{8\pi}{5} \times \frac{180}{\pi}\).

Simplify the expression by canceling \(\pi\) in numerator and denominator: \(-\frac{8}{5} \times 180\).

Multiply the numbers to find the degree measure (do not calculate the final value here, just set up the multiplication).

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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 subtended at the center of a circle by an arc equal in length to the radius. Radians provide a natural way to measure angles in terms of the circle's geometry.

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 related to radians through a fixed conversion factor.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the fact that π radians equal 180 degrees. For example, to convert -8π/5 radians, multiply by 180/π to get the equivalent angle in degrees.