In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places. 2 radians

Verified step by step guidance

1. Recall the conversion formula from radians to degrees: \(\text{degrees} = \text{radians} \times \frac{180}{\pi}\).
2. Substitute the given angle in radians into the formula: \(2 \times \frac{180}{\pi}\).
3. Multiply the numerator: \(2 \times 180 = 360\), so the expression becomes \(\frac{360}{\pi}\).
4. Divide 360 by the value of \(\pi\) (approximately 3.14159) to get the angle in degrees.
5. Round the resulting value to two decimal places to complete the conversion.

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 through the circle's total angle of 2π 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 are related to radians by the conversion factor 180° = π radians.

Conversion Between Radians and Degrees

To convert radians to degrees, multiply the radian value by 180/π. This formula allows you to express an angle measured in radians as degrees, which is often easier to interpret. For example, 2 radians × (180/π) gives the angle in degrees.