In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.15°

Verified step by step guidance

1. Understand that to convert degrees to radians, you use the conversion factor \( \frac{\pi}{180} \).
2. Multiply the given angle in degrees by the conversion factor: \( 15° \times \frac{\pi}{180} \).
3. Simplify the expression by multiplying the numbers: \( \frac{15\pi}{180} \).
4. Reduce the fraction by finding the greatest common divisor of 15 and 180, which is 15.
5. Divide both the numerator and the denominator by 15 to simplify the fraction.

Key Concepts

Degrees and Radians

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 one to the other.

Conversion Formula

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

Multiples of π

When expressing angles in radians, it is common to represent them as multiples of π. This means that the radian measure is written in the form of kπ, where k is a rational number. This format is particularly useful in trigonometric functions and helps simplify expressions.