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.

Q1:

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

  • A radians
  • B radians
  • C radians
  • D radians
  • E radians

  • A radians
  • B radians
  • C radians
  • D radians
  • E radians

  • A radians
  • B radians
  • C radians
  • D radians
  • E radians

Q2:

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

radians

  • A
  • B
  • C
  • D
  • E

radians

  • A
  • B
  • C
  • D
  • E

radians

  • A
  • B
  • C
  • D
  • E

Q3:

What is the equivalent size of in radians?

  • A
  • B
  • C
  • D
  • E

Q4:

Convert 3 6 0 to radians giving the answer in terms of 𝜋 .

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

Q5:

Two angles in a triangle are 5 5 and 7 𝜋 1 8 r a d i a n s . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

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

Q6:

The shadow of a sundial changes at a rate of 1 5 every hour. After how many hours will the shadow have rotated by an angle of 𝜋 radians?

Q7:

Convert 1 0 5 into radians in terms of 𝜋 .

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

Q8:

Find the values of two supplementary angles in radians given the difference between the angles is 𝜋 4 5 .

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

Q9:

Two angles in a triangle are 𝜋 6 and 8 𝜋 1 5 . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

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

Q10:

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

  • A 2 3 𝜋 3 6 r a d
  • B 1 7 𝜋 1 2 r a d
  • C 4 9 𝜋 3 6 r a d
  • D 7 𝜋 1 2 r a d

Q11:

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

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

What is the angle of a complete rotation?

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

What is the length of the arc in a unit circle subtended by an angle of 𝜋 4 ?

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

Which fraction of a complete rotation does an angle of 𝜋 4 correspond to?

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

Q12:

Convert 6 0 to radians giving the answer in terms of 𝜋 .

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

Q13:

Convert 7 0 into radians in terms of 𝜋 .

  • A 7 0 𝜋
  • B 7 0 𝜋
  • C 7 𝜋 3 6
  • D 7 𝜋 1 8
  • E 1 8 𝜋 7

Q14:

Two angles in a triangle are 2 0 and 1 1 𝜋 3 6 r a d i a n s . Find the value of the third angle giving the answer in radians in terms of 𝜋 .

  • A 7 𝜋 6
  • B 1 1 𝜋 3 6
  • C 1 1 𝜋 1 8
  • D 7 𝜋 1 2

Q15:

The shadow of a sundial changes at a rate of 1 5 every hour. After how many hours will the shadow have rotated by an angle of 𝜋 4 radians?

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