In Exercises 35–40, convert each angle in radians to degrees. Round to two decimal places.𝜋/13 radians

Verified step by step guidance

1. Understand the conversion factor: To convert radians to degrees, use the conversion factor \( \frac{180}{\pi} \).
2. Set up the conversion: Multiply the given angle in radians by the conversion factor. So, \( \frac{\pi}{13} \times \frac{180}{\pi} \).
3. Simplify the expression: The \( \pi \) in the numerator and denominator will cancel out, leaving \( \frac{180}{13} \).
4. Perform the division: Divide 180 by 13 to find the angle in degrees.
5. Round the result: Round the quotient to two decimal places to get the final answer in degrees.

Key Concepts

Radians and Degrees

Radians and degrees are two units for measuring angles. A radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. There are 2π radians in a full circle, which corresponds to 360 degrees. Thus, to convert between these units, one can use the relationship: 180 degrees = π radians.

Conversion Formula

To convert an angle from radians to degrees, the formula used is: degrees = radians × (180/π). This formula allows for a straightforward calculation by multiplying the radian measure by the fraction that relates the two units. For example, to convert π/13 radians to degrees, you would multiply π/13 by 180/π, simplifying the calculation.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, rounding to two decimal places means that the final answer should be expressed with two digits after the decimal point. This is important for clarity and precision in mathematical communication, especially when dealing with measurements and conversions.