Describe 𝜃=𝜋/9 by an angle of negative radian measure by determining the angle 𝛼 that is coterminal with 𝜃=𝜋/9 if −2𝜋<𝛼<0.

Question

(Give an exact answer in units of radians. Use symbolic notation and fractions where needed.) 𝛼= ____rad

Answer 1

Starting at "0" which is the green line above (positive "x-axis") going counterclockwise is a positive angle (blue) and going clockwise is a negative angle (red).

Going from the start, all the way around and back to the start again is 2π radians.

If you go +π/9 radians, you will be going counterclockwise (blue direction) and you will be going 1/18 of the way around the circle (so just a little bit). To go to the same place coming from the other direction (red direction) you would need to go just π/9 short of all the way around. 2π - π/9 = 18π/9 - π/9 = 17π/9 but since you are going in the clockwise (red) direction, you will be going -17π/9 radians. Doing so will put you right on top of the same location as if you went +π/9.