In Exercises 13–20, convert each angle in degrees to radians. Express your answer as a multiple of 𝜋.330°

Verified step by step guidance

1. Understand the relationship between degrees and radians: 180° is equivalent to \( \pi \) radians.
2. To convert degrees to radians, use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
3. Substitute 330° into the formula: \( 330° \times \frac{\pi}{180} \).
4. Simplify the fraction \( \frac{330}{180} \) by finding the greatest common divisor of 330 and 180.
5. Express the simplified fraction 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 an angle from degrees to radians, you can use the formula: radians = degrees × (π/180). This formula allows you to express the angle in terms of π, which is often required in trigonometric contexts.

Multiples of π

When expressing angles in radians, it is common to represent them as multiples of π. For example, an angle of π/6 radians corresponds to 30 degrees. This representation simplifies calculations in trigonometry and helps in understanding the properties of angles.