# Worksheet: Introduction to Radians

In this worksheet, we will practice converting angles from degrees to radians and vice-versa and use your understanding of radians to solve problems.

**Q4: **

Convert to radians giving the answer in terms of .

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**Q5: **

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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**Q6: **

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?

**Q7: **

Convert into radians in terms of .

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**Q8: **

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

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

**Q9: **

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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**Q10: **

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

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**Q11: **

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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**Q12: **

Convert to radians giving the answer in terms of .

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**Q13: **

Convert into radians in terms of .

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- E

**Q14: **

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

- A
- B
- C
- D

**Q15: **

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?