#include <cmath>
#include <map>

double cachedSin(double angle)
{
    static std::map<double, double> results;
    std::map<double, double>::iterator i;

    i = results.find(angle);

    if (i != results.end())
    {
        return i->second;
    } else {
        double result = sin(angle);
        results[angle] = result;
        return result;
    }
}