Question

Approximate sin (12π)/13 by using a linear approximation with f (x) =sin x.

Answer 1

http://tinychat.com/trevort1997

Answer 2

Note that a = 3π/12 = π/4 is close to 3π/13, with h = π/4 - 3π/13 = π/52.

Now, we compute c.
f(x) = cos x, f '(x) = -sin x.

Thus, cos (3π/13) ≈ cos(π/4) + (-sin(π/4)) · π/52 ≈ 0.664 (to three decimal places).
(i.e., c ≈ 0.664.)