What angle (in radians) corresponds to 0.75 rotations around the unit circle?


(Give an exact answer as a fraction.)

Verified Answer :

3pi/2. The unit circle is 2pi

Using proportions, it is found that an angle of \(1.5\pi\) corresponds to 0.75 rotations around the unit circle

  • This question can be solved by proportions, using a rule of three.
  • An entire rotation is of \(2\pi\) radians. What is the angle of 0.75 rotations?

The rule of three is:

1 rotation - \(2\pi\) radians

0.75 rotations - x radians

Applying cross multiplication:

\(x = 2\pi(0.75) = 1.5\pi\)

An angle of \(1.5\pi\) corresponds to 0.75 rotations around the unit circle

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