I having a trigonometric function such as
$$ p_2(s) =
\begin{cases}
\frac {1}{(2 \pi)^2}(1-\cos (2 \pi s)), & \text{if $s \le1$ } \\
\frac {1}{2 }(s-1)^2, & \text{if $s >1$ }
\end{cases}$$
The function has two minimum points $s =1$ and $s= 0$. The figure of the above function such as
However, the computational time is more expensive. To reduce it, one guy proposed a approximate function using polynomial such as $$ p_2(s) = \begin{cases} \frac {1}{2}s^2(s-1)^2+\frac {1}{2}s^3(s-1)^3, & \text{if $s \le1$ } \\ \frac {1}{2 }(s-1)^2, & \text{if $s >1$ } \end{cases}$$
He said that his method is trigonometric representation because he used polynomial. Is it right? Could you suggest to me other representation that has similar properties of above function. Thanks