Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 60°

Verified step by step guidance

1. Recall the formula to convert degrees to radians: \(\text{radians} = \text{degrees} \times \frac{\pi}{180}\).
2. Substitute the given degree measure into the formula: \(60^\circ \times \frac{\pi}{180}\).
3. Simplify the fraction \(\frac{60}{180}\) by dividing numerator and denominator by their greatest common divisor, which is 60.
4. After simplification, express the result as a multiple of \(\pi\).
5. Write the final answer in radians as a simplified fraction times \(\pi\).

Key Concepts

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 answers as multiples of π keeps the results exact and simplifies further calculations in trigonometry.

Simplifying Fractions

After converting degrees to radians, the resulting fraction involving π should be simplified to its lowest terms. Simplification makes the expression clearer and easier to interpret, such as converting 60° to π/3 radians.