Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―900°

Verified step by step guidance

1. Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
2. Substitute the given degree measure into the formula: \(-900^\circ \times \frac{\pi}{180}\).
3. Simplify the fraction by dividing both numerator and denominator by their greatest common divisor.
4. Express the result as a multiple of \(\pi\) without calculating the decimal value.
5. Write the final answer in the form \(\frac{\text{integer}}{\text{integer}} \pi\).

Key Concepts

Degree to Radian Conversion

Degrees and radians are two units for measuring angles. To convert degrees to radians, multiply the degree measure by π/180. This conversion is essential because radians are the standard unit in many trigonometric applications.

Understanding Negative Angles

Negative angles represent rotation in the clockwise direction, opposite to the positive (counterclockwise) direction. When converting, the sign is preserved, indicating the direction of rotation, which is important for interpreting the angle correctly.

Expressing Answers as Multiples of π

Leaving answers as multiples of π means writing the radian measure in terms of π rather than decimal approximations. This exact form is preferred in trigonometry for clarity and precision, such as writing -900° as -5π radians.