How to remember the unit circle?

Question

If you are enrolled in a Pre-Calculus or Calculus Course your must remember the Unit Circle. In this video, I will show you how to never forget the unit circle in just 5 minutes.

Answer 1

First, go around the circle in 4 parts, starting at 0, and proceeding counter-clockwise.

You have 0, π/2, π, 3π/2, 2π. In degrees, this is 0, 90, 180, 270, and 360 degrees. The coordinate pairs on the unit circle corresponding to these angular values are (0,1), (1,0), (-1,0), (0,-1), and (0,0).

Next, start at 45 degrees, and take steps of 90 degrees each time. That's 45, 135, 225, and 315 degrees. In radians, that is π/4, 3π/4, 5π/4, and 7π/4. The coordinate pairs on the unit circle corresponding to thes values are (√2/2,√2/2), (-√2/2,√2/2), (-√2/2,-√2/2), and (√2/2,-√2/2).

Next, start at 30 degrees, then add 120 degrees, then add 60 degrees, then add 120 degrees. That's 30, 150, 210, and 330 degrees. In radians, that's π/6, 5π/6, 7π/6, and 11π/6. The corresponding coordinate pairs are (√3/2, 0.5), (-√3/2, 0.5), (-√3/2, -0.5), and (√3/2, -0.5).

Finally, start at 60 degrees, then add 60 degrees, next add 120 degrees, then add 60 degrees: 60, 120, 240, 300 degrees. In radians, that is π/3, 2π/3, 4π/3, and 5π/3. The corresponding coordinate pairs on the unit circle are (0.5, √3/2), (-0.5, √3/2), (-0.5, -√3/2), and (0.5, -√3/2).

Answer 2

Below I linked to a short video explaining the topic :)

https://www.loom.com/share/b5acb0c3cfd64662b0d1f6b56548eda9?sid=14a5c476-1a22-49b0-a291-2121ec356e48