Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).

42.5°

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: \(42.5^\circ \times \frac{\pi}{180}\).

Simplify the fraction by multiplying the numerator and denominator: \(\frac{42.5 \pi}{180}\).

Calculate the decimal value of the fraction \(\frac{42.5}{180}\) to get a decimal multiplier for \(\pi\).

Multiply the decimal by \(\pi\) (approximately 3.14159) and round the result to the nearest thousandth if required.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

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 mathematical contexts, especially calculus and trigonometry.

Use of π in Radian Measures

Radians are often expressed in terms of π because the circumference of a circle relates to π. For example, 180° equals π radians. Understanding this relationship helps in converting and simplifying angle measures in radians.

Rounding to the Nearest Thousandth

After converting degrees to radians, the result may be an irrational number. Rounding to the nearest thousandth means keeping three decimal places, which balances precision and simplicity for practical use.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).42.5°