Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°

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: \(30^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{30}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 30.

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

Write the final answer in the form \(\frac{\pi}{n}\) where \(n\) is the simplified denominator.

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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 angles as multiples of π provides exact values rather than decimal approximations.

Simplifying Radicals and Fractions

After converting degrees to radians, simplify the resulting fraction to its lowest terms. This makes the answer clearer and easier to interpret, especially when expressing the radian measure as a multiple of π.