Find the linearization L(x) of the function

Question

a) f(x) = sin(x) at x = pi/3

b) Use L(x) from part a) to approximate sin (1).

Answer 1

L(x) = f(π/3) + f'(π/3)(x - π/3) = sin(π/3) + cos(π/3)(x - π/3) = (√3/2) + (1/2)(x - π/3)

sin(1) = f(1) ≈ L(1) = (√3/2) + (1/2)(1 - π/3) = 0.842426628