A sinusoid with an amplitude of 5 and wave length of 10 can be defined with the following equations:

x = 10*t

y(t) = 5*sin(u) 

u(t) = 2*pi*t

The third equation is necessary since "t" must be between zero and one and we want an entire period of the sine wave, from 0–2π.

Auxiliary functions such as this can be defined. By using two auxiliary variable-value equations for the amplitude and wave length a more flexible definition results.

x = wl*t;
y = amp*sin(u);
u = 2*pi*t;
amp = 5;
wl = 10;

This definition could be used to place sine waves of any amplitude and wave length by modifying the last two equations. It is clear, however, that the first three equations should not be modified, since doing that would corrupt the sine wave's definition.