In Exercises 2–4, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.315°

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: \( 315° \times \frac{\pi}{180} \).
3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.
4. Express the simplified fraction as a multiple of \( \pi \).
5. Verify that the angle is correctly expressed in radians as a multiple of \( \pi \).

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

Expressing angles in radians as multiples of π is a common practice in trigonometry. This format simplifies calculations and helps in understanding the relationship between angles and their trigonometric functions, as many key angles correspond to simple fractions of π.