Question

find an equation to the curve at the point corresponding to the given value of the parameter.
x = tcost y = tsint when t = π

i know I am supposed to find dy and dx which is:

dy = (product form) t*-sint + 1*cost
simplifying = -tsint+cost

dx = tcost+sint

now, to find the I realize it is simply just dy/dx

which equals -tsint+cost/tcost+sint

however slope intercept form is y-y1=m(x-x1) right?

Answer 1

no, that is point-slope form.

To me, it's just as good as the slop-intercept form, since it contains all the necessary info.

For this kind of problem, you have a point on the curve, and the slope of the tangent. The point-slope form is ideal.

x = tcost
dx/dt = cost - tsint

y = tsint
dy/dt = sint - tcost

dy/dx = -π