Convert each degree measure to radians. Leave answers as multiples of π. See Examples 1(a) and 1(b). ​​ ―315°

Verified step by step guidance

1. Start with the formula to convert degrees to radians: \( \text{radians} = \text{degrees} \times \frac{\pi}{180} \).
2. Substitute the given degree measure into the formula: \(-315° \times \frac{\pi}{180} \).
3. Simplify the expression by multiplying \(-315\) by \(\frac{\pi}{180}\).
4. Factor out the greatest common divisor from \(-315\) and \(180\) to simplify the fraction.
5. Express the simplified fraction as a multiple of \(\pi\).

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 the angle subtended at the center of a circle by an arc equal in length to the radius. 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.

Negative Angles in Trigonometry

In trigonometry, angles can be positive or negative, with negative angles indicating a clockwise rotation from the positive x-axis. For example, -315° is equivalent to a positive angle of 45° (since -315° + 360° = 45°). Understanding how to interpret and convert negative angles is important for solving trigonometric problems accurately.