CPM Homework Help : APCALC Problem 12-32

Write the equation of a second-degree polynomial to approximate $f(x) = \sin(x)$ near $x =\frac { \pi } { 2 }$ .

Step 1:

$f\Big(\frac{\pi}{2}\Big)=\sin\Big(\frac{\pi}{2}\Big)=1$

$f^\prime\Big(\frac{\pi}{2}\Big)=\cos\Big(\frac{\pi}{2}\Big)=0$

$f^{\prime\prime}\Big(\frac{\pi}{2}\Big)=-\sin\Big(\frac{\pi}{2}\Big)=-1$

Step 2:

$p_2(x)=1+0\Big(x-\frac{\pi}{2}\Big)-\frac{1\Big(x-\frac{\pi}{2}\Big)^2}{2!}$