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

Verified step by step guidance

1. Recall the formula to convert an angle from radians to degrees: \(\text{Degrees} = \text{Radians} \times \frac{180}{\pi}\).
2. Identify the given angle in radians, which is \(\frac{7\pi}{5}\).
3. Substitute the given radian measure into the conversion formula: \(\frac{7\pi}{5} \times \frac{180}{\pi}\).
4. Simplify the expression by canceling out \(\pi\) in the numerator and denominator: \(\frac{7 \times 180}{5}\).
5. Perform the multiplication and division to find the angle in degrees (this is the final calculation step you can do on your own).

Key Concepts

Radian Measure

A 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. Understanding radians is essential because many trigonometric functions use radians as their standard input.

Degree Measure

Degrees are a common unit for measuring angles, where a full circle is divided into 360 equal parts. Converting radians to degrees involves understanding that 360 degrees correspond to 2π radians, which allows for conversion between these two units.

Conversion Formula Between Radians and Degrees

To convert radians to degrees, multiply the radian measure by 180/π. This formula comes from the equivalence of 2π radians to 360 degrees. Applying this formula to the given angle 7π/5 will yield its degree measure.