# Worksheet: Conversion between Radians and Degrees

In this worksheet, we will practice converting radians to degrees and vice versa.

**Q2: **

Convert 0.5 rad to degrees giving the answer to the nearest second.

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**Q3: **

Convert rad to degrees giving the answer to the nearest second.

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**Q4: **

A gymnast circles a pommel horse by an angle of . Find the angle in radians giving the answer to one decimal place.

**Q5: **

Find the values of two angles in degrees given their sum is and their difference is . Give the answer to the nearest degree.

- A ,
- B ,
- C ,
- D ,

**Q6: **

Find the values of two angles in radians given their sum is and their difference is . Give the answer to two decimal places.

- A 0.47 rad, 1.17 rad
- B 0.3 rad, 1.17 rad
- C 0.47 rad, 0.99 rad
- D 0.3 rad, 0.99 rad

**Q7: **

Convert to radians giving the answer to three decimal places.

**Q8: **

The shadow of a sundial changes at a rate of every hour. Find the angle of the shadow’s position 5 hours after sunrise giving the answer in radians to three decimal places.

**Q9: **

Convert to radians giving the answer in terms of .

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**Q12: **

Convert into radians in terms of .

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**Q13: **

Find the size of the smaller angle between the hour and minute hands at half past nine giving the answer in radians.

- A rad
- B rad
- C rad
- D rad

**Q14: **

Two angles in a triangle are and . Find the value of the third angle giving the answer in radians in terms of .

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- D

**Q15: **

Two angles in a triangle are and . Find the value of the third angle giving the answer in radians in terms of .

- A
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- D

**Q17: **

What is the perimeter of a unit circle in terms of ?

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What is the angle of a complete rotation?

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What is the length of the arc in a unit circle subtended by an angle of ?

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Which fraction of a complete rotation does an angle of correspond to?

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**Q18: **

Find the values of two supplementary angles in radians given the difference between the angles is .

- A ,
- B ,
- C ,
- D ,

**Q19: **

The shadow of a sundial changes at a rate of every hour. After how many hours will the shadow have rotated by an angle of radians?

**Q20: **

Which of the following is equal to ?

- A
- B
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- D