maths

f(x) = x + sin|x|
a)sketch f(x) in the interval -2pi <= x <= 2pi with your calculation.
b)find the tangent to f(x) at x = pi
c)there is a circle C with centre P(x,y).C always touch f(x) at point x with
the radius which always equal to the value of |f(x)| at point x.Find the locus of P.