This is quite hard to explain haha but I'll try my best

Firstly I'm pretty sure that is a graph of EMF vs time, but they are just showing the angles on the graph, i.e. the axis are still EMF and Time.

If you were to sketch a graph of magnetic flux vs time it would be a cosine curve, as you mentioned in the first image magnetic flux is max and then at 90 degrees it is min(this process continues).

Now EMF is the negative time derivative of the magnetic flux. So if the magnetic flux vs time is a cosine curve, then EMF vs time should be a sine curve which is what you see.

I had the same kind of questions that caused problems for my schools Physics department because HSC Physics is soo brief when teaching such concepts because well no CALCULUS allowed.

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