How to Convert Radians to Degrees

Step-by-step solution

1. Multiply the radians by 180 over pi.

   $$\frac{5\pi}{6} \times \frac{180^\circ}{\pi}$$

   Why: A full turn is 2 pi radians or 360 degrees, so the factor between them is 180 over pi.

2. Cancel pi and multiply.

   $$\frac{5 \times 180^\circ}{6} = \frac{900^\circ}{6}$$

   Why: Pi appears on the top and the bottom, so it cancels.

3. Divide to finish the conversion.

   $$\frac{900^\circ}{6} = 150^\circ$$

   Why: 900 divided by 6 is 150.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\frac{\pi}{3}$

   Show answer

   $60^\circ$

2. 2

   $\frac{\pi}{4}$

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   $45^\circ$

3. 3

   $\frac{3\pi}{2}$

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   $270^\circ$

4. 4

   $2\pi$

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   $360^\circ$

5. 5

   $\frac{7\pi}{6}$

   Show answer

   $210^\circ$