Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°

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: \(60^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{60}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 60.

After simplification, express the result as a multiple of \(\pi\).

Write the final answer in radians as a simplified fraction times \(\pi\).

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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 π as a Constant

π (pi) is an irrational constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. Expressing answers as multiples of π keeps the results exact and simplifies further calculations in trigonometry.

Simplifying Fractions

After converting degrees to radians, the resulting fraction involving π should be simplified to its lowest terms. Simplification makes the expression clearer and easier to interpret, such as converting 60° to π/3 radians.