Worksheet: Conversion between Radians and Degrees

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

Q1:

Convert 𝜋3 to degrees.

  • A 1 2 0 ∘
  • B 1 . 0 4 7 ∘
  • C 6 0 ∘
  • D 3 0 0 ∘

Q2:

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

  • A 2 8 3 8 ′ 5 2 ′ ′ ∘
  • B 9 0 ∘
  • C 5 7 1 7 ′ 4 5 ′ ′ ∘
  • D 0 3 1 ′ ′ ∘
  • E 0 9 ′ 3 3 ′ ′ ∘

Q3:

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

  • A 3 5 9 5 6 ′ 3 3 ′ ′ ∘
  • B 3 4 1 5 0 ′ 5 2 ′ ′ ∘
  • C 1 7 0 5 5 ′ 2 6 ′ ′ ∘
  • D 3 5 8 5 6 ′ 5 8 ′ ′ ∘
  • E 1 2 6 ∘

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.

  • A 6 2 ∘ , 2 2 ∘
  • B 5 2 ∘ , 2 2 ∘
  • C 6 2 ∘ , 3 2 ∘
  • D 6 2 ∘ , 1 2 ∘

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.

  • 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 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.

  • A 𝜋 2
  • B 2 𝜋
  • C 3 6 0 𝜋
  • D 3 6 0 𝜋
  • E 𝜋

Q10:

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

9 0 ∘

  • A 𝜋 2 radians
  • B 𝜋 4 radians
  • C 𝜋 5 radians
  • D 𝜋 3 radians
  • E 𝜋 6 radians

3 0 ∘

  • A 𝜋 3 radians
  • B 𝜋 4 radians
  • C 𝜋 5 radians
  • D 𝜋 2 radians
  • E 𝜋 6 radians

5 5 ∘

  • A 1 1 𝜋 3 6 radians
  • B 2 𝜋 3 radians
  • C 𝜋 5 radians
  • D 𝜋 6 radians
  • E 3 𝜋 4 radians

Q11:

What is the equivalent measure of 360∘ in radians?

  • A 2 𝜋
  • B 𝜋 2
  • C 4 𝜋
  • D 3 𝜋
  • E 𝜋

Q12:

Convert −105∘ into radians in terms of 𝜋.

  • A − 1 2 𝜋 7
  • B − 1 0 5 𝜋
  • C − 7 𝜋 1 2
  • D − 7 𝜋 2 4
  • E − 1 0 5 𝜋

Q13:

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

  • A 1 7 𝜋 1 2 rad
  • B 2 3 𝜋 3 6 rad
  • C 4 9 𝜋 3 6 rad
  • D 7 𝜋 1 2 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.

  • A 1 1 𝜋 3 6
  • B 1 1 𝜋 1 8
  • C 7 𝜋 9
  • D 7 𝜋 1 8

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.

  • A 𝜋 5
  • B 1 6 𝜋 4 5
  • C 3 𝜋 1 0
  • D 𝜋 6

Q16:

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

𝜋 3 radians

𝜋 7 radians

3 𝜋 8 radians

Q17:

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

  • A 4 𝜋
  • B 𝜋 2
  • C 𝜋
  • D 𝜋 4
  • E 2 𝜋

What is the angle of a complete rotation?

  • A 𝜋
  • B 𝜋 2
  • C 3 𝜋
  • D 𝜋 4
  • E 2 𝜋

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

  • A 𝜋 8
  • B 𝜋
  • C 4 𝜋
  • D 𝜋 2
  • E 𝜋 4

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

  • A 1 8
  • B 1 4
  • C 1 2
  • D 1 1 6
  • E 3 4

Q18:

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

  • A 2 3 𝜋 4 5 , 2 2 𝜋 4 5
  • B 4 1 𝜋 9 0 , 2 2 𝜋 4 5
  • C 2 3 𝜋 4 5 , 4 9 𝜋 9 0
  • D 4 1 𝜋 9 0 , 4 9 𝜋 9 0

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?

  • A s i n ( 1 2 6 ) ∘
  • B s i n  1 3 1 0 𝜋 
  • C s i n  1 1 0 𝜋 
  • D s i n ( − 1 2 6 ) ∘

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