Hi, I'm puzzled by the following, and wondering what am I missing:
x = r cos(theta)
y = r sin(theta)
r = sqrt(x^2+y^2)
up to +-pi: theta = arctan(y/x)
we get:
dx/dtheta = -r sin(theta)
dtheta/dx = 1/(1+y^2/x^2) * (-y/x^2) = -y/(x^2 + y^2) = -sin(theta)/r
if we use the inverse function derivative (for a constant r) we get a contradiction, since 1/(r sin(theta) != sin(theta)/r
What has happened here?
Thanks a lot!
x = r cos(theta)
y = r sin(theta)
r = sqrt(x^2+y^2)
up to +-pi: theta = arctan(y/x)
we get:
dx/dtheta = -r sin(theta)
dtheta/dx = 1/(1+y^2/x^2) * (-y/x^2) = -y/(x^2 + y^2) = -sin(theta)/r
if we use the inverse function derivative (for a constant r) we get a contradiction, since 1/(r sin(theta) != sin(theta)/r
What has happened here?
Thanks a lot!