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

122° 37'

검증된 단계별 안내

Understand that to convert degrees to radians, we use the formula: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

First, convert the given angle from degrees and minutes to a decimal degree. Recall that 1 minute (') is equal to \(\frac{1}{60}\) of a degree, so convert 37' to degrees by calculating \(37 \times \frac{1}{60}\).

Add the decimal degree value from the minutes to the whole degrees: \(122 + \left(37 \times \frac{1}{60}\right)\) to get the total degrees in decimal form.

Multiply the decimal degree value by \(\frac{\pi}{180}\) to convert it to radians: \(\left(122 + \frac{37}{60}\right) \times \frac{\pi}{180}\).

If needed, use a calculator to approximate the radian value and round it 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 trigonometric applications.

Converting Minutes to Decimal Degrees

Angle measurements often include minutes (') where 1 degree equals 60 minutes. To convert minutes to decimal degrees, divide the minutes by 60 and add this to the degree value. This step is necessary before converting the total degrees to radians.

Rounding to the Nearest Thousandth

After converting 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 in calculations.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).122° 37'