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Sunday, February 12, 2012

The Unit of Circle

This is just a little recapitulation of the unit of circle and the formulas.

The variable "t" is the number of quarter-turns.

These formulas are for the clockwise rotations of the segments/arrows.
I've viewed the voicethread and shuffled things up and manipulated some things a bit to come up with these formulas. Hope they help you!


These are the formulas for the counter-clockwise part of the unit of the circle.

Thank-you for reading!


  1. I really love the amount of effort you put into your blogs to make everything simpler for everyone... well if not for everyone, certainly clears things up for me :) Although is this about the b17 voicethread or the circle unit ?! :O

    1. Hehehe thanks! :3
      Um, well, at the beginning it was supposed to be for the B17, but I think I ended up making a post for mainly the circle unit. D:

  2. Joey on behalf of everyone, students AND teachers, thank you for doing this and helping it make sense to people. I have a few questions, which maybe we'll get to in class today but here they are just in case:
    In your first two diagrams, you used the variable t. Does this variable stand for the number of quarter-circles your arm has rotated through?
    In your last two diagrams, you used the same variable, but does it stand for the number of full-circle rotations here (because you switched to 360 instead of 90...) or still quarter-circle rotations?
    Finally, in the last two diagrams, it looks like your starting point for the angles was not at the same place as it was for the first two diagrams - did I interpret your diagram correctly? If so, then this post is definitely about unit circle angles in general, because the B17's always start at the positive x-axis.
    Wonderful, wonderful, post!

    1. I have corrected each and every problem. Sorry for any unfortunate outcomes.