In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋. 315°

검증된 단계별 안내

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

Substitute the given angle 315° into the formula: \(315 \times \frac{\pi}{180}\).

Simplify the fraction \(\frac{315}{180}\) by finding the greatest common divisor (GCD) of 315 and 180.

Divide both numerator and denominator by the GCD to reduce the fraction to its simplest form.

Express the final answer as a multiple of \(\pi\) using the simplified fraction.

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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 resulting fraction should be simplified to its lowest terms. This involves reducing the numerator and denominator by their greatest common divisor to express the angle neatly as a multiple of π.