Approximate cos (2π/13) by using a linear approximation with

Question

f (x) =cos x.

cos (2π/13)≈ f(a) + f ' (a)·h = c,

what is h, a, and c? I'm having problems with this one please help

Answer 1

You want to pick a value of cos(x) where x is near 2π/13, and you know what it is.

you know cos(π/6) = √3/2. 2π/13 = π/6 - π/156, which is pretty close to π/6.

cos(2π/13) ≈ cos(π/6)+(-sin(π/6))(π/156)
= √3/2 - (1/2)(π/156)
= 0.8560

the true value is 0.8855

That seems kind of far off, but remember that at π/6 the curve is fairly sharply curved, so the linear approximation will not be too close.