In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 15°

검증된 단계별 안내

Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).

Substitute the given angle in degrees (15°) into the formula: \(15 \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{15}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 15.

After simplification, express the result as a multiple of \(\pi\) in the form \(\frac{1}{12} \pi\).

Write the final answer as \(\frac{\pi}{12}\) radians.

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주요 개념

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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.

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 a precise and standardized way to represent radian measures.

Simplifying Radicals and Fractions

After converting degrees to radians, the result should be simplified as a fraction multiplied by π. Simplifying fractions ensures the answer is in its simplest form, making it easier to interpret and use in further calculations.