- #1
elegysix
- 406
- 15
given an ellipse in vector form
r(phi)=a*cos(phi)i +b*sin(phi)j
where i and j are the unit vectors for x and y,
then y= b*sin(phi), and x = a*cos(phi).
tan(phi) = y / x ,
but y/x=(b/a)*tan(phi)
which implies 1 = b/a or b=a
which is false.
What is the deal?
doing the same for a circle leads to the true statement, 1=1.
r(phi)=a*cos(phi)i +b*sin(phi)j
where i and j are the unit vectors for x and y,
then y= b*sin(phi), and x = a*cos(phi).
tan(phi) = y / x ,
but y/x=(b/a)*tan(phi)
which implies 1 = b/a or b=a
which is false.
What is the deal?
doing the same for a circle leads to the true statement, 1=1.