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

56° 25'

검증된 단계별 안내

Understand that to convert degrees and minutes to radians, you first need to convert the entire angle into decimal degrees. Recall that 1 minute (') is equal to \( \frac{1}{60} \) degrees.

Convert the given angle 56° 25' into decimal degrees using the formula: \( \text{Decimal degrees} = 56 + \frac{25}{60} \).

Use the conversion factor between degrees and radians: \( 1^{\circ} = \frac{\pi}{180} \) radians. Multiply the decimal degree value by \( \frac{\pi}{180} \) to convert to radians.

Write the expression for the angle in radians as \( \left(56 + \frac{25}{60}\right) \times \frac{\pi}{180} \).

If required, calculate the numerical value of the radians 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 calculations.

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 part. This step ensures the angle is expressed as a single decimal degree value before converting 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. This is important for practical applications where exact values are not necessary.

Convert each degree measure to radians. If applicable, round to the nearest thousandth. See Example 1(c).56° 25'