The following problem problem I need help with:-

The parametric curve de ned by the equations

x

(t) = cos(t); y(t) = sin(3t); 0 <=t <= 2:

a) Find a formula which represents the slope of the tangent line to the curve at the point (

x(t); y(t)):

b) Find the points (values of

t and corresponding (x; y) coordinates) where the curve has a horizontal tangent line, and nd the points where the curve has a vertical tangent line.

c) Use the information you found in part b) to draw a sketch of the curve.

d) Set-up, but do not compute, an integral that represents the length of this parametric curve.