Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). 30°

Verified step by step guidance

1. Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).
2. Multiply the degree measure by the conversion factor: \( 30° \times \frac{\pi}{180} \).
3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
4. Recognize that the simplified fraction will give you the radian measure as a multiple of \( \pi \).
5. Express the final answer in terms of \( \pi \), ensuring it is in its simplest form.

Key Concepts

Degree and Radian Measure

Degrees and radians are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. Understanding the relationship between these two units is essential for converting angles from degrees to radians and vice versa.

Conversion Formula

To convert degrees to radians, the formula used is: radians = degrees × (π/180). This formula allows for the straightforward conversion of any angle measured in degrees into its corresponding radian measure, facilitating calculations in trigonometry.

Multiples of π

When expressing angles in radians, it is common to leave the answer as a multiple of π. For example, 30° converts to π/6 radians. This notation emphasizes the relationship between the angle and the circle's circumference, making it easier to work with in trigonometric functions.