Local Linearization of f(x) = cosx at a = $\pi$/2

[Mirole]

f(x) = cosx, a = $$\pi$$/2
since, L(x)=f'(x)(x-a) -f(a)
f'(x) = -sinx
= -sin($$\pi$$/2)(x-$$\pi$$/2) - f(a)


I'm stuck as to where to go next, is this even right?

 

[Mirole]

Nevermind, I got it to be -x+$$\pi$$/2, which is correct!