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.

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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 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°, converting degrees to radians often results in fractions involving π, which should be left in this form for exactness and clarity.

Simplifying Fractions

After converting degrees to radians, the resulting fraction should be simplified to its lowest terms. This makes the radian measure easier to interpret and use in further calculations, ensuring the answer is presented in the simplest exact form.