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

Verified step by step guidance

1. Understand the relationship between radians and degrees: 180 degrees is equivalent to \( \pi \) radians.
2. To convert an angle from radians to degrees, use the formula: \( \text{degrees} = \text{radians} \times \frac{180}{\pi} \).
3. Substitute the given angle \(-3\pi\) into the formula: \( \text{degrees} = -3\pi \times \frac{180}{\pi} \).
4. Simplify the expression by canceling out \( \pi \) from the numerator and the denominator.
5. Multiply the remaining numbers to find the angle in degrees.

Key Concepts

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert between these units, the relationship can be used: 180 degrees equals π radians. Understanding this relationship is essential for converting angles accurately.

Conversion Formula

The conversion from radians to degrees can be performed using the formula: degrees = radians × (180/π). This formula allows for straightforward calculations when converting any angle expressed in radians to its degree equivalent, ensuring clarity in angular measurements.

Negative Angles

Negative angles indicate a rotation in the clockwise direction. When converting a negative radian measure, such as -3π, to degrees, the same conversion principles apply. Recognizing the significance of negative angles is important for understanding their position and direction in the coordinate system.