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### Course: Pixar in a Box>Unit 14

Lesson 2: Mathematics of rotation

# 3. Completing the proof

In this video, we'll discuss the geometry of rotation. We can find the new coordinates of a point after it's been rotated around the origin using the concepts of sine, cosine, and similar triangles to derive the formulas for the new coordinates.

## Want to join the conversation?

• yo I don't get any of this
• How can you come up with the equation x'=x*cosθ - y*sinθ
from:
x'=sqrt(x^2 + y^2) * cos(θ + arccos(x/sqrt(x^2 + y^2))) ?
Thanks
• At , there was a thing that was saying how they made a mistake in the formula when they wrote it down, but I didn't even notice cuz I was so confused about the equation in da first place lol XD
• Is there a way to calculate coordinates for rotating around another point? not just the origin?
(1 vote)
• translate to the origin, rotate and translate back with the inverse of the original translation
• What about for 3 dimensional objects?
(1 vote)
• I'm taking the rigging class and I cannot figure out how to complete this problem

blank = x * cos( blank ) - y * sin( blank );
blank = x * sin( blank ) + y * cos( blank );
• The blanks inside `cos()` and `sin()` will be the angle, in this case, `value`. The first line calculates the value for `coordinate.x`, the second for `coordinate.y`.