Question

Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation.

x^2cos^2y - siny = 0

Note: I forgot the ^2 for cos on the previous question. Sorry.

Answer 1

x = 0, y = pi

-x^2 2 cos y sin y dy +cos^2y 2 x dx - cos y dy = 0

2 cos^2 y x dx=cosy (2x^2siny+1)dy

dy/dx = slope m

m = 2 x cos y/(2x^2siny+1)
at (0,pi)
m = 2 * 0 = 0 Oh my :) horizontal there
so what is y at x = 0 and y = pi
LOL, zero
so along the x axis

Answer 2

I mean parallel to x axis and y = pi
for part 2, normal is up the y axis
see
http://www.wolframalpha.com/widgets/view.jsp?id=91851988c40ebbe236f5561e167c9ab8

Answer 3

Just copy your function into there:
x^2cos^2y - siny = 0

look at the solution close to (0,0)