3. In this question, you can use a calculator or a computer to compute the maximum error.
(a) Find the piecewise linear interpolation for $\sin x$ with the node points $0, \pm \frac{\pi}{6}, \pm \frac{\pi}{3}, \pm \frac{\pi}{2}, \dots$
That is, give a formula for the interpolating piecewise linear function $l(x)$. Compute
as precisely as possible, the maximum error of this interpolation.
(b) Find the quadratic interpolation polynomial for $\cos x$ with the node points $0, \pm \frac{\pi}{2}$.
Compute as precisely as possible, the maximum error of this interpolation in the
interval $[ -\frac{\pi}{2}, \frac{\pi}{2}] $.
