In Exercises 5–7, convert each angle in radians to degrees. - 5𝜋 6

Verified step by step guidance

1. Recall the conversion formula from radians to degrees: \(\text{Degrees} = \text{Radians} \times \dfrac{180}{\pi}\).
2. Identify the given angle in radians: \(\dfrac{5\pi}{6}\).
3. Substitute the given angle into the conversion formula: \(\dfrac{5\pi}{6} \times \dfrac{180}{\pi}\).
4. Simplify the expression by canceling \(\pi\) in numerator and denominator: \(\dfrac{5}{6} \times 180\).
5. Multiply the remaining numbers to find the angle in degrees: \(5 \times \dfrac{180}{6}\).

Key Concepts

Radian Measure

Radian is a unit of angular measure based on the radius of a circle. One radian is the angle subtended at the center of a circle by an arc equal in length to the radius. It provides a natural way to measure angles in terms of the circle's geometry.

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, making it intuitive for everyday use and practical applications.

Conversion between Radians and Degrees

To convert radians to degrees, multiply the radian value by 180/π. This conversion factor arises because π radians equal 180 degrees. For example, converting 5π/6 radians involves multiplying by 180/π to find the equivalent degree measure.