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Worksheet: Introduction to Radians

Q1:

What is the equivalent measure of 3 6 0 ∘ in radians?

  • A 3 πœ‹
  • B πœ‹
  • C πœ‹ 2
  • D 2 πœ‹
  • E 4 πœ‹

Q2:

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

9 0 ∘

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

3 0 ∘

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

5 5 ∘

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

Q3:

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

πœ‹ 3 radians

πœ‹ 7 radians

3 πœ‹ 8 radians

Q4:

Convert 3 6 0 ∘ to radians giving the answer in terms of πœ‹ .

  • A 3 6 0 πœ‹
  • B 3 6 0 πœ‹
  • C πœ‹
  • D 2 πœ‹
  • E πœ‹ 2

Q5:

Convert 6 0 ∘ to radians giving the answer in terms of πœ‹ .

  • A 6 0 πœ‹
  • B 6 0 πœ‹
  • C πœ‹ 6
  • D πœ‹ 3
  • E 3 πœ‹

Q6:

Convert βˆ’ 1 0 5 ∘ into radians in terms of πœ‹ .

  • A βˆ’ 1 0 5 πœ‹
  • B βˆ’ 1 0 5 πœ‹
  • C βˆ’ 7 πœ‹ 2 4
  • D βˆ’ 7 πœ‹ 1 2
  • E βˆ’ 1 2 πœ‹ 7

Q7:

Convert βˆ’ 7 0 ∘ into radians in terms of πœ‹ .

  • A βˆ’ 7 0 πœ‹
  • B βˆ’ 7 0 πœ‹
  • C βˆ’ 7 πœ‹ 3 6
  • D βˆ’ 7 πœ‹ 1 8
  • E βˆ’ 1 8 πœ‹ 7

Q8:

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œ‹ 3 6 r a d
  • B 1 7 πœ‹ 1 2 r a d
  • C 4 9 πœ‹ 3 6 r a d
  • D 7 πœ‹ 1 2 r a d

Q9:

Two angles in a triangle are 5 5 ∘ and 7 πœ‹ 1 8 . Find the value of the third angle giving the answer in radians in terms of πœ‹ .

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

Q10:

Two angles in a triangle are 2 0 ∘ and 1 1 πœ‹ 3 6 . Find the value of the third angle giving the answer in radians in terms of πœ‹ .

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

Q11:

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

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

Q12:

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

  • A πœ‹ 2
  • B πœ‹
  • C πœ‹ 4
  • D 2 πœ‹
  • E 4 πœ‹

What is the angle of a complete rotation?

  • A 2 πœ‹
  • B πœ‹ 2
  • C 3 πœ‹
  • D πœ‹
  • E πœ‹ 4

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

  • A πœ‹ 8
  • B 4 πœ‹
  • C πœ‹ 4
  • D πœ‹
  • E πœ‹ 2

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

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

Q13:

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

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

Q14:

The shadow of a sundial changes at a rate of 1 5 ∘ every hour. After how many hours the shadow will rotate by an angle of πœ‹ radians?

Q15:

The shadow of a sundial changes at a rate of 1 5 ∘ every hour. After how many hours the shadow will rotate by an angle of πœ‹ 4 radians?