Worksheet: Conversion between Radians and Degrees

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

Q1:

Convert 𝜋3 to degrees.

Q2:

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

  • A90∘
  • B09′33′′∘
  • C031′′∘
  • D2838′52′′∘
  • E5717′45′′∘

Q3:

Convert −3.3 rad to degrees giving the answer to the nearest second.

  • A126∘
  • B17055′26′′∘
  • C35956′33′′∘
  • D35856′58′′∘
  • E34150′52′′∘

Q4:

A gymnast circles a pommel horse by an angle of 50∘. 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 74∘ and their difference is 𝜋6. Give the answer to the nearest degree.

  • A52∘, 22∘
  • B62∘, 22∘
  • C62∘, 12∘
  • D62∘, 32∘

Q6:

Find the values of two angles in radians given their sum is 74∘ and their difference is 2𝜋9. Give the answer to two decimal places.

  • A0.3 rad, 1.17 rad
  • B0.47 rad, 0.99 rad
  • C0.3 rad, 0.99 rad
  • D0.47 rad, 1.17 rad

Q7:

Convert 14246′48′′∘ to radians giving the answer to three decimal places.

Q8:

The shadow of a sundial changes at a rate of 15∘ 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 360∘ to radians giving the answer in terms of 𝜋.

  • A360𝜋
  • B𝜋2
  • C𝜋
  • D2𝜋
  • E360𝜋

Q10:

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

90∘

  • A𝜋4 radians
  • B𝜋5 radians
  • C𝜋3 radians
  • D𝜋6 radians
  • E𝜋2 radians

30∘

  • A𝜋4 radians
  • B𝜋6 radians
  • C𝜋2 radians
  • D𝜋3 radians
  • E𝜋5 radians

55∘

  • A11𝜋36 radians
  • B𝜋6 radians
  • C𝜋5 radians
  • D2𝜋3 radians
  • E3𝜋4 radians

Q11:

What is the equivalent measure of 360∘ in radians?

  • A2𝜋
  • B𝜋2
  • C𝜋
  • D3𝜋
  • E4𝜋

Q12:

Convert −105∘ into radians in terms of 𝜋.

  • A−7𝜋24
  • B−7𝜋12
  • C−12𝜋7
  • D−105𝜋
  • E−105𝜋

Q13:

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

  • A49𝜋36 rad
  • B23𝜋36 rad
  • C17𝜋12 rad
  • D7𝜋12 rad

Q14:

Two angles in a triangle are 55∘ and 7𝜋18radians. Find the value of the third angle giving the answer in radians in terms of 𝜋.

  • A7𝜋18
  • B11𝜋18
  • C7𝜋9
  • D11𝜋36

Q15:

Two angles in a triangle are 𝜋6 and 8𝜋15. Find the value of the third angle giving the answer in radians in terms of 𝜋.

  • A𝜋6
  • B3𝜋10
  • C16𝜋45
  • D𝜋5

Q16:

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

𝜋3 radians

𝜋7 radians

3𝜋8 radians

Q17:

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

  • A4𝜋
  • B𝜋2
  • C𝜋
  • D𝜋4
  • E2𝜋

What is the angle of a complete rotation?

  • A𝜋
  • B𝜋2
  • C3𝜋
  • D𝜋4
  • E2𝜋

What is the length of the arc in a unit circle subtended by an angle of 𝜋4?

  • A𝜋8
  • B𝜋
  • C4𝜋
  • D𝜋2
  • E𝜋4

Which fraction of a complete rotation does an angle of 𝜋4 correspond to?

  • A18
  • B14
  • C12
  • D116
  • E34

Q18:

Find the values of two supplementary angles in radians given the difference between the angles is 𝜋45.

  • A41𝜋90, 49𝜋90
  • B23𝜋45, 49𝜋90
  • C41𝜋90, 22𝜋45
  • D23𝜋45, 22𝜋45

Q19:

The shadow of a sundial changes at a rate of 15∘ every hour. After how many hours will the shadow have rotated by an angle of 𝜋 radians?

Q20:

Which of the following is equal to sin−1310𝜋?

  • Asin1310𝜋
  • Bsin(126)∘
  • Csin110𝜋
  • Dsin(−126)∘

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