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)
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
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.