Convert each radian measure to degrees. See Examples 2(a) and 2(b). π/3

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, which is \(\frac{\pi}{3}\).
3. Substitute the radian value into the conversion formula: \(\frac{\pi}{3} \times \frac{180}{\pi}\).
4. Simplify the expression by canceling out \(\pi\) in the numerator and denominator.
5. Calculate the remaining fraction \(\frac{180}{3}\) to find the degree measure.

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 formula 2π radians = 360 degrees.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Each degree represents 1/360 of a full rotation. Degrees are often used in practical applications and are convertible to radians using a fixed ratio.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This ratio comes from the equivalence of 2π radians to 360 degrees. For example, π/3 radians equals (π/3) × (180/π) = 60 degrees.