# Worksheet: Conversion between Radians and Degrees

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

Q1:

Convert to degrees.

Q2:

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

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Q3:

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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.

Q7:

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:

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Q10:

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

Q11:

What is the equivalent measure of in radians?

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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.

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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Q15:

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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Q16:

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

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 ?

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• D