Originally Posted by

**nzmathman** Here's a challenge: for the function $\displaystyle y= a\,\sin{(bx+c)} + d$, find a polynomial of degree 3 (ie a cubic) approximation for y on the interval from one trough to one peak (about the main original point of inflection) - eg for $\displaystyle y=\sin{(x)} $ that interval would be $\displaystyle \left[-\frac{\pi}{2}, \,\frac{\pi}{2}\right]$

Express the answer in the form $\displaystyle y = px^3+qx^2+rx+s$, where p, q , r and s are in terms of a, b, c and d.