Convert between Degrees and Radians Worksheets - Free Printable

Let's solve the problem step by step.

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A) Convert each degree measure to radian measure

To convert degrees to radians, use the formula:

$$
\text{radians} = \text{degrees} \times \frac{\pi}{180}
$$

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1) $ 250^\circ $

$$
250 \times \frac{\pi}{180} = \frac{250\pi}{180} = \frac{5\pi}{3.6} = \frac{25\pi}{18}
$$

✔ Answer: $ \frac{25\pi}{18} $

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2) $ -360^\circ $

$$
-360 \times \frac{\pi}{180} = -2\pi
$$

✔ Answer: $ -2\pi $

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3) $ 64^\circ $

$$
64 \times \frac{\pi}{180} = \frac{64\pi}{180} = \frac{16\pi}{45}
$$

✔ Answer: $ \frac{16\pi}{45} $

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4) $ -9^\circ $

$$
-9 \times \frac{\pi}{180} = -\frac{9\pi}{180} = -\frac{\pi}{20}
$$

✔ Answer: $ -\frac{\pi}{20} $

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5) $ 32^\circ $

$$
32 \times \frac{\pi}{180} = \frac{32\pi}{180} = \frac{8\pi}{45}
$$

✔ Answer: $ \frac{8\pi}{45} $

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6) $ -171^\circ $

$$
-171 \times \frac{\pi}{180} = -\frac{171\pi}{180} = -\frac{19\pi}{20}
$$

✔ Answer: $ -\frac{19\pi}{20} $

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7) $ 900^\circ $

$$
900 \times \frac{\pi}{180} = 5\pi
$$

✔ Answer: $ 5\pi $

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8) $ -783^\circ $

$$
-783 \times \frac{\pi}{180} = -\frac{783\pi}{180}
$$

Simplify:

Divide numerator and denominator by 3:

$$
-\frac{261\pi}{60}, \quad \text{again by 3: } -\frac{87\pi}{20}
$$

✔ Answer: $ -\frac{87\pi}{20} $

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9) $ 45^\circ $

$$
45 \times \frac{\pi}{180} = \frac{45\pi}{180} = \frac{\pi}{4}
$$

✔ Answer: $ \frac{\pi}{4} $

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B) Convert each radian measure to degree measure

Use the formula:

$$
\text{degrees} = \text{radians} \times \frac{180}{\pi}
$$

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1) $ -\frac{11\pi}{6} $

$$
-\frac{11\pi}{6} \times \frac{180}{\pi} = -\frac{11}{6} \times 180 = -330^\circ
$$

✔ Answer: $ -330^\circ $

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2) $ \frac{\pi}{2} $

$$
\frac{\pi}{2} \times \frac{180}{\pi} = \frac{1}{2} \times 180 = 90^\circ
$$

✔ Answer: $ 90^\circ $

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3) $ -\frac{31\pi}{18} $

$$
-\frac{31\pi}{18} \times \frac{180}{\pi} = -\frac{31}{18} \times 180 = -31 \times 10 = -310^\circ
$$

✔ Answer: $ -310^\circ $

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4) $ \pi $

$$
\pi \times \frac{180}{\pi} = 180^\circ
$$

✔ Answer: $ 180^\circ $

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5) $ -\frac{3\pi}{10} $

$$
-\frac{3\pi}{10} \times \frac{180}{\pi} = -\frac{3}{10} \times 180 = -54^\circ
$$

✔ Answer: $ -54^\circ $

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6) $ \frac{43\pi}{60} $

$$
\frac{43\pi}{60} \times \frac{180}{\pi} = \frac{43}{60} \times 180 = 43 \times 3 = 129^\circ
$$

✔ Answer: $ 129^\circ $

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7) $ \frac{5\pi}{12} $

$$
\frac{5\pi}{12} \times \frac{180}{\pi} = \frac{5}{12} \times 180 = 5 \times 15 = 75^\circ
$$

✔ Answer: $ 75^\circ $

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8) $ \frac{7\pi}{3} $

$$
\frac{7\pi}{3} \times \frac{180}{\pi} = \frac{7}{3} \times 180 = 7 \times 60 = 420^\circ
$$

✔ Answer: $ 420^\circ $

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9) $ -4\pi $

$$
-4\pi \times \frac{180}{\pi} = -4 \times 180 = -720^\circ
$$

✔ Answer: $ -720^\circ $

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✔ Final Answers:

#### A) Degrees to Radians
1) $ \frac{25\pi}{18} $
2) $ -2\pi $
3) $ \frac{16\pi}{45} $
4) $ -\frac{\pi}{20} $
5) $ \frac{8\pi}{45} $
6) $ -\frac{19\pi}{20} $
7) $ 5\pi $
8) $ -\frac{87\pi}{20} $
9) $ \frac{\pi}{4} $

#### B) Radians to Degrees
1) $ -330^\circ $
2) $ 90^\circ $
3) $ -310^\circ $
4) $ 180^\circ $
5) $ -54^\circ $
6) $ 129^\circ $
7) $ 75^\circ $
8) $ 420^\circ $
9) $ -720^\circ $

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