This is homework. I need to calculate the derivative of this function found by using the cubic spline bounded.
The original approx is used to calculate sin, the question asked is $cos 0.34$
$S(x) = 0.31457 + 0.71244(x-0.32) + 15.6149(x-0.32)^2 - 262.80741(x-0.32)^3$
so I thought about plugging in $S'(0.34)$ to find $cos 0.34$ This didn't work.
I have all the values of the derivatives for the original equation. I could construct a new cubic spline for cos but this is just inefficient. Is there a more efficient way of doing this?