The parametric equations of a curve are x = cos 4A + 2cos 2A, y = sin 4A - 2sin2A where A is the parameter. Find (a ) dy/dx and (b) equation of the normal to the curve at the point where A = pi/4
For part a) you need to use the Chain Rule.
Recall that .
.
So
.
For part b) , you need to remember that a normal is a LINE.
So it is of the form .
At the point ...
.
The gradient of the curve at point A is
.
The gradient of the normal is the negative reciprocal. So .
Thus the normal's equation is given by
.
Hope that helped.