Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ 1800°

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 degree measure by the conversion factor: \( 1800° \times \frac{\pi}{180} \).
3. Simplify the expression by dividing 1800 by 180.
4. The result will be a multiple of \( \pi \).
5. Express the simplified result as a multiple of \( \pi \).

Key Concepts

Degree to Radian Conversion

To convert degrees to radians, use the conversion factor π radians = 180 degrees. This means that to convert a degree measure to radians, you multiply the degree value by π/180. For example, 180 degrees is equivalent to π radians, and this relationship is fundamental in trigonometry for working with angles.

Understanding π

The symbol π (pi) represents the ratio of the circumference of a circle to its diameter, approximately equal to 3.14159. In trigonometry, π is crucial for expressing angles in radians, as many trigonometric functions are defined in terms of radians rather than degrees. Recognizing π as a constant helps in simplifying expressions involving angles.

Multiples of π

When expressing angles in radians, it is common to leave answers as multiples of π. This means that instead of providing a decimal approximation, the angle is expressed in terms of π, such as kπ, where k is a rational number. This form is often preferred in trigonometry for clarity and precision, especially in theoretical contexts.