Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 1800°

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: \(1800^\circ \times \frac{\pi}{180}\).

Simplify the fraction by dividing 1800 by 180: \(\frac{1800}{180} = 10\).

Express the result as a multiple of \(\pi\): \(10\pi\) radians.

Therefore, the degree measure \(1800^\circ\) is equivalent to \(10\pi\) radians.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

도움이 되었나요?

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.

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 in terms of π allows for exact values rather than decimal approximations, which is useful in trigonometric calculations.

Simplifying Radicals and Fractions

After converting degrees to radians, the resulting fraction should be simplified by dividing numerator and denominator by their greatest common divisor. This simplification makes the radian measure clearer and easier to interpret, especially when expressed as a multiple of π.