Use differentials (linear approximation) to estimate sin(-2).?

Question

Base the approximation at x= -2pi/3

Answer 1

f(x) = f(a)+(x-a) f´(a)
sin(-2) = sin (-2pi/3)+(-2+2pi/3) *cos(-2pi/3) =-0.8660-0.5*0.0944=0,9132
The real value is -0.9093