Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

Question

x=tcos(t), y=tsin(t); t=π

Answer 1

the slope is

dy/dx = (dy/dt)/(dx/dt)
= (sint + tcost)/(cost - t sint)
y'(π) = (0-π)/(-1-0) = π

at t=π, x=-π and y=0

so, using the point slope form of the line,

y = π(x+π)