The local linear approximation of f near x = a is given by
f(x) ≈ f(a) + f'(a)(x-a)
Evaluating f at π/2
f(π/2) = cos(π/2) = 0
Since f(x) = cos(x), differentiating gets us
f'(x) = -sin(x)
f'(π/2) = -sin(π/2) = -1
So the local liner approximation is
f(x) ≈ 0+ -1(x-π/2)
f(x) ≈ -x+π/2
The answer to this question is -x+π/2
