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

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: \(-300^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{-300}{180}\) by dividing numerator and denominator by their greatest common divisor.

Express the result as a multiple of \(\pi\), keeping the negative sign if applicable.

Write the final answer in the form \(\frac{a\pi}{b}\), where \(a\) and \(b\) are integers with no common factors.

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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. When converting negative degrees to radians, the sign is preserved, indicating the direction of rotation. This helps in correctly interpreting angle measures in trigonometry.

Expressing Answers as Multiples of π

Leaving answers as multiples of π means writing the radian measure in the form (aπ/b), where a and b are integers. This exact form is preferred over decimal approximations to maintain precision and clarity in trigonometric expressions.