In Exercises 5–7, convert each angle in radians to degrees.- 5𝜋6

Verified step by step guidance

1. Start with the conversion formula: Degrees = Radians × \( \frac{180}{\pi} \).
2. Substitute the given radian value into the formula: \( 5\pi/6 \times \frac{180}{\pi} \).
3. Simplify the expression by canceling out \( \pi \) from the numerator and denominator.
4. Multiply the remaining numbers: \( 5/6 \times 180 \).
5. Calculate the product to find the angle in degrees.

Key Concepts

Radians and Degrees

Radians and degrees are two units for measuring angles. A full circle is 360 degrees or 2π radians. To convert between these units, the relationship is established: 180 degrees equals π radians. Understanding this relationship is essential for converting angles accurately.

Conversion Formula

The conversion from radians to degrees can be done using the formula: degrees = radians × (180/π). This formula allows for straightforward calculations when converting any angle expressed in radians to its equivalent in degrees, ensuring clarity in angular measurements.

Multiplication of Fractions

When converting angles, it often involves multiplying fractions. For example, when converting 5π/6 radians to degrees, you multiply 5π/6 by 180/π. Understanding how to simplify and multiply fractions is crucial for obtaining the correct degree measure from the radian value.