Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 3600°

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: \(3600^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{3600}{180}\) by dividing numerator and denominator by their greatest common divisor.

Express the result as a multiple of \(\pi\) after simplification.

Write the final answer in the form \(k\pi\), where \(k\) is the simplified numerical coefficient.

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 Multiples of π

Expressing angles as multiples of π simplifies the representation of radian measures. Since π radians equal 180°, writing answers in terms of π helps maintain exact values without decimal approximations, which is important for precision in trigonometric calculations.

Simplification of Fractions

After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure clearer and easier to interpret, especially when dealing with large degree values like 3600°, ensuring the answer is concise and exact.