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

Q1:

Convert the following angle sizes from degrees to radians. Give your answers in terms of in their simplest form.

Q2:

Convert the following angle sizes from radians to degrees. Give your answers to the nearest degree where necessary.

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Q3:

What is the equivalent size of in radians?

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Q4:

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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 .

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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:

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Q13:

Convert into radians in terms of .

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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:

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?