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 \( \frac{\pi}{180} \).
3. For the given problem, multiply \(-1800°\) by \( \frac{\pi}{180} \).
4. Simplify the expression by dividing \(-1800\) by \(180\) to find the multiple of \(\pi\).
5. Express the result as a simplified fraction multiplied by \(\pi\).

Key Concepts

Degree to Radian Conversion

To convert degrees to radians, use the formula: radians = degrees × (π/180). This relationship arises from the definition of a radian, which is based on the radius of a circle. Understanding this conversion is essential for solving problems that require angle measures in different units.

Understanding π (Pi)

Pi (π) is a mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter. In trigonometry, π is often used in angle measures, particularly when converting between degrees and radians. Recognizing π as a fundamental part of radian measures is crucial for accurate calculations.

Multiples of π

When expressing angles in radians, it is common to leave answers as multiples of π, such as nπ, where n is a rational number. This notation simplifies expressions and calculations in trigonometry, making it easier to work with angles in various mathematical contexts. Understanding how to manipulate and interpret these multiples is key to solving trigonometric problems.