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

85.04°

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: \(85.04^\circ \times \frac{\pi}{180}\).

Multiply the degree value by \(\pi\) to get \(85.04 \times \pi\) in the numerator.

Divide the result by 180 to complete the conversion to radians.

If needed, use a calculator to approximate the value and round the result to the nearest thousandth.

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 is 2π times its radius. This relationship makes π a natural constant in angle measurement, linking linear and angular dimensions. Understanding this helps interpret radian values both symbolically and numerically.

Rounding to the Nearest Thousandth

After converting degrees to radians, the result may be an irrational number. Rounding to the nearest thousandth means limiting the decimal places to three digits, which balances precision and simplicity. This is important for practical applications where exact values are unnecessary or unavailable.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).85.04°