Homework 1b.

4. Suppose \(y = -cosx\).
a) Take the derivative of y with respect to x. Use a substitution to write that as a function of y.
b) Plot \(\frac{\partial y}{\partial x }\) as a function of y from y =-1 to 1.
c) Plot \(1/|\frac{\partial y}{\partial x }|\) as a function of y from y =-1 to 1.
d) Can you integrate \(1/|\frac{\partial y}{\partial x }|\) as a function of y from y =-1 to 1? If so, what do you get?
PS. Please email what you get for part d. You can add some brief description of the salient features in your email as well if you like.