Worksheet: Conversion between Radians and Degrees

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

Q1:

Convert 𝜋 3 to degrees.

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

Q2:

Convert 0 . 5 r a d to degrees giving the answer to the nearest second.

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

Q3:

Convert − 3 . 3 r a d to degrees giving the answer to the nearest second.

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

Q4:

A gymnast circles a pommel horse by an angle of 5 0 ∘ . 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 7 4 ∘ and their difference is 𝜋 6 . Give the answer to the nearest degree.

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

Q6:

Find the values of two angles in radians given their sum is 7 4 ∘ and their difference is 2 𝜋 9 . Give the answer to two decimal places.

  • A 0 . 4 7 r a d , 0 . 9 9 r a d
  • B 0 . 3 r a d , 1 . 1 7 r a d
  • C 0 . 4 7 r a d , 1 . 1 7 r a d
  • D 0 . 3 r a d , 0 . 9 9 r a d

Q7:

Convert 1 4 2 4 6 ′ 4 8 ′ ′ ∘ to radians giving the answer to three decimal places.

Q8:

The shadow of a sundial changes at a rate of 1 5 ∘ every hour. Find the angle of the shadow’s position 5 hours after sunrise giving the answer in radians to three decimal places.

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