# Interpolation of trigonometric functions

I want to evaluate $f''(x)$ for $f(x)=\sin(x)$ and $x=\frac{\pi}{6}$ and then determine the error in the approximation of $f''(\frac{\pi}{6})$.

From previous knowledge, I know that to find an approximation, we need to compute the first derivative to represent the change. Since the question requires the second derivative, I'm a little confused. I appreciate any assistance.

• Are you sure $f''=-f$ perhaps in Taylor series of $\sin$. – Nosrati Apr 17 '17 at 12:05
• Yes. that is true – Ben Apr 17 '17 at 12:07

HINT: $f^{"}(x)=-\sin x$.
Treat this as $y=f^{"}(x)$
Then simply $$\frac{dy}{dx}=\frac{\Delta y}{\Delta x}$$