Convert each degree measure to radians. Leave answers as multiples of π.

175°

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: \(175^\circ \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{175}{180}\) by finding the greatest common divisor (GCD) of 175 and 180.

Express the simplified fraction multiplied by \(\pi\) to write the answer as a multiple of \(\pi\).

Write the final answer in the form \(\frac{a}{b} \pi\), where \(a\) and \(b\) are the simplified numerator and denominator.

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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 as multiples of π provides an exact and simplified form, which is preferred over decimal approximations in trigonometry.

Simplifying Fractions in Angle Conversion

After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. Simplification makes the expression clearer and easier to work with in further calculations, such as solving trigonometric equations or evaluating functions.

Convert each degree measure to radians. Leave answers as multiples of π.175°