Question

The linearization approximation for sin(x) about r=0 ?

Answer 1

Take f(x) = sin x, then
f'(x) = cos x and f(0) = 0

f'(0) = 1, f(x) ≈ f(0) + f'(0)(x − 0) = 0 + 1.x
So using basepoint x0 = 0, f(x) = x.

Answer 2

That's not an accurate estimate though...
i.e sin(.5) doesn't equal .5 in fact not even close
tried it for other numbers to it's not true