Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 1800°

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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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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.

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Converting between Degrees & Radians

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 in terms of π allows for exact values rather than decimal approximations, which is useful in trigonometric calculations.

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Simplifying Radicals and Fractions

After converting degrees to radians, the resulting fraction should be simplified by dividing numerator and denominator by their greatest common divisor. This simplification makes the radian measure clearer and easier to interpret, especially when expressed as a multiple of π.

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