1. ## Parametric equations.

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.

2. [QUOTE=Sally_Math;500410]
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)):

The "slope of the tangent line" is $\displaystyle \frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

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.

The tangent line will be horizontal when $\displaystyle \frac{dy}{dt}= 0$ and vertical when $\displaystyle \frac{dx}{dt}= 0$.

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.

$\displaystyle \int \sqrt{(\frac{dx}{dt})^2+ \frac{dy}{dt})^2} dt$