Question

Find the equation of the line tangent to the parametric curve define by
x=cos2t and y=sin3t and t=pi/12
plz i don't no where to start from show working

Answer 1

first, find the slope of the tangent line at any point:

dy/dx = (dy/dt)/(dx/dt)
Yes, these really are fractions!
dy/dx = (3cos3t)/(-2sin2t)
Now, at t=pi/2, the point on the curve is (0,-1), and the slope is 0

So, our tangent is the line

y+1 = 0(x-0)
or
y = -1

See the curve at

http://www.wolframalpha.com/input/?i=parametric+plot+x%3Dcos2t+and+y%3Dsin3t