In Exercises 21–28, convert each angle in radians to degrees. -3𝜋

Verified step by step guidance

1. Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \dfrac{180}{\pi}\).
2. Identify the given angle in radians, which is \(-3\pi\).
3. Substitute the given angle into the conversion formula: \(-3\pi \times \dfrac{180}{\pi}\).
4. Simplify the expression by canceling \(\pi\) in the numerator and denominator: \(-3 \times 180\).
5. Multiply the numbers to find the angle in degrees (do not calculate the final value here, just set up the expression).

Key Concepts

Radian Measure

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. It is a fundamental unit in trigonometry, where 2𝜋 radians equal 360 degrees.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree is further divided into 60 minutes and each minute into 60 seconds. Degrees are often used in practical applications and are related to radians by 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 -3𝜋 radians, multiply -3𝜋 by 180/𝜋 to get -540 degrees.