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

검증된 단계별 안내

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

Substitute the given degree measure into the formula: \(-900^\circ \times \frac{\pi}{180}\).

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor.

Express the result as a multiple of \(\pi\) without calculating the decimal value.

Write the final answer in the form \(\frac{\text{integer}}{\text{integer}} \pi\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.