In Exercises 5–7, convert each angle in radians to degrees. 5𝜋 3

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

Identify the given angle in radians: \(\frac{5\pi}{3}\).

Substitute the given angle into the conversion formula: \(\frac{5\pi}{3} \times \frac{180}{\pi}\).

Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\frac{5 \times 180}{3}\).

Perform the division and multiplication to find the angle in degrees.

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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. Radians provide a natural way to measure angles in terms of the circle's geometry, and many trigonometric functions use radians as their standard input.

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, converting 5π/3 radians to degrees involves multiplying 5π/3 by 180/π, simplifying to 300 degrees.