Linear Approximation

Question

Use the standard linearization to estimate sin(0.02).

Answer 1

I assume the argument 0.02 is in radians.

f(x + Δx) ≅ f(x) + f'(x)Δx

f(x) = sin(x)

x = 0

Δx =0.02

f'(x) = cos(x)

sin(0 + 0.02) ≅ sin(0) + cos(0)(0.02) = 0 + 1(0.02) = 0.02

This result is consistent with the approximation

sin(x) ≅ x when x << 1 (x in radians).