Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ―315°

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: \(-315^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{315}{180}\) by finding the greatest common divisor (GCD) of 315 and 180, which is 45.

Divide numerator and denominator by 45 to simplify the fraction: \(\frac{315}{180} = \frac{7}{4}\).

Write the final expression for the radian measure as \(-\frac{7\pi}{4}\).

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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 the angle's position on the unit circle.

Expressing Answers as Multiples of π

Leaving answers as multiples of π means expressing 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 -315° as -7π/4 radians.