Convert each radian measure to degrees.


5π/4

Verified step by step guidance

1. Recall the conversion formula between radians and degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
2. Identify the given radian measure: \(\frac{5\pi}{4}\).
3. Substitute the radian value into the conversion formula: \(\frac{5\pi}{4} \times \frac{180}{\pi}\).
4. Simplify the expression by canceling out \(\pi\) in the numerator and denominator: \(\frac{5}{4} \times 180\).
5. Multiply the remaining numbers to find the degree measure: \(5 \times \frac{180}{4}\).

Key Concepts

Radian Measure

A radian is a unit of angular measure based on the radius of a circle. One radian is the angle created when the arc length equals the radius. It is a standard unit in trigonometry and is related to degrees by the conversion factor 180° = π radians.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Degrees are often used in practical applications and can be converted to radians using the relationship 1 radian = 180/π degrees.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This conversion uses the equivalence of π radians to 180 degrees, allowing you to express angles in the more familiar degree unit.