tangent line on curve is negative of expected

Hi. I think I've reversed a sign somewhere, but for the life of me I can't seem to find it.

I have these parametric equations (using t to represent theta):

I've got to find the equation of the tangent line at various given points on the curve. So, I want to create a general equation first that I can plug the points into. First, I solve for t:

Then I get the slope:

Now, the intercept in the tangent line equation will be

Giving me

or

Great. But if I plug in the first coordinate I'm given

I eventually get

A tangent line with a negative slope! Yet when I look diagram provided in the book itself, the tangent line at this point clearly has a positive slope.

Re: tangent line on curve is negative of expected

Hey infraRed.

Given your parametric model, you have:

dy/dt = 2cos(t) and

dx/dt = 3sin(t) which means

dy/dx = dy/dt / dx/dt = 2/3 * cot(t)

Re: tangent line on curve is negative of expected

Wow. I think I'm going to shoot myself now.