Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―300°

Verified step by step guidance

1. Start with the formula to convert degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
2. Substitute the given degree measure into the formula: \(-300° \times \frac{\pi}{180} \).
3. Simplify the fraction: \(-300 \div 180 = -\frac{300}{180} \).
4. Reduce the fraction to its simplest form: \(-\frac{5}{3} \).
5. Multiply the simplified fraction by \(\pi\) to express the answer as a multiple of \(\pi\): \(-\frac{5}{3}\pi\).

Key Concepts

Degree and Radian Measures

Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is essential for converting angles from one measure to another.

Conversion Formula

To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the direct conversion of any angle measured in degrees into its corresponding radian measure, facilitating calculations in trigonometry.

Multiples of π

When expressing angles in radians, it is common to leave the answer as a multiple of π. This means that instead of providing a decimal approximation, the angle is expressed in terms of π, which maintains precision and is often preferred in mathematical contexts.