Finding equation of a path in the plane

Jaylyn Villarreal

Jaylyn Villarreal

Answered question

2022-04-06

Finding equation of a path in the plane y=z
What is the easiest way to see that the path r:RR3:t(sin,t,cos,t,cos,t)
traces out an ellipse in the plane y=z?
I think first rotating R3 by π4 about the x-axis will help but I am not sure how to proceed.

Answer & Explanation

stecchiniror7

stecchiniror7

Beginner2022-04-07Added 14 answers

Explanation:
The rotation by π4 will yield the path
(x,y,z)=(sint,2cost,0)
in the new coordinates. How do you eliminate t? Use sin2t+cos2t=1:
x2+y22=1

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?