Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―7π/20

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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: \(-\frac{7\pi}{20}\).

Substitute the radian value into the conversion formula: \(-\frac{7\pi}{20} \times \frac{180}{\pi}\).

Simplify the expression by canceling \(\pi\) in numerator and denominator: \(-\frac{7}{20} \times 180\).

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.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion works because 180 degrees is equivalent to π radians. For example, to convert -7π/20 radians, multiply by 180/π to get the degree measure.

Simplifying Fractional Angles

When converting angles expressed as fractions of π, it is important to simplify the fraction after multiplication to get a clear degree value. This often involves multiplying numerators and denominators and reducing the fraction to its simplest form for easier interpretation.