# Zero Frequency Basis Equation for Discrete Sine Transform

So, I'm evaluating the Discrete Sine transform Basis functions and I found on the internet the following picture:

So, I may be getting the point wrong, but, if the 2D DCT equation is:

Then the Discrete Sine transform shall be:

Then, it is clear that for the lower frequency (u=0,v=0) all cosines will be 1, but in the case of the sines all will be 0 (for frequency=0), therefore, the basis function for the lower frequency, in the sine case, will be zero, right?

Is the upper left image (u=0,v=0) correct? It should be constant, right? (btw: It shall also be zero, right?)