Question

Given the parametric curve x= sin(2t) and y=2 sin(t)+ sin(2t)

1) Calculate the slope of the tangent line at any value of t.
2) Find the tangent line at t= (1/2)(Pi).

Answer 1

the slope of the tangent line is

dy/dx = (dy/dt)/(dx/dt) = (2cost + 2cos(2t))/(2cos(2t))
Now plug in your point.