In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. 2 radians

검증된 단계별 안내

Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).

Substitute the given angle in radians into the formula: \(2 \times \frac{180}{\pi}\).

Multiply the numerator: \(2 \times 180 = 360\), so the expression becomes \(\frac{360}{\pi}\).

Divide 360 by the value of \(\pi\) (approximately 3.14159) to get the angle in degrees.

Round the resulting value to two decimal places to complete the conversion.

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주요 개념

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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 through the circle's total angle of 2π 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 are related to radians by the conversion factor 180° = π radians.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian value by 180/π. This formula allows you to express an angle measured in radians as degrees, which is often easier to interpret. For example, 2 radians × (180/π) gives the angle in degrees.