Hello xwrathbringerx

If I had asked for a sketch of the graph of , I would expect to see a diagram showing:

- and axes, including both positive and negative values of and .

- a sine wave centred on , showing at least part of a cycle for negative values of , and at least, say, one-and-a-half cycles for positive .

- points and marked on , with the sine wave having corresponding maximum and minimum values
- an indication on the diagram of the phase shift, given by the value of ; in other words, the sine wave passing through a point marked as .

I think I'd also expect to see some reference to the fact that the diagram shows the case where and .

For a fuller answer, you could obviously also sketch what happens if either or both of and is negative. Clearly, there would then no need to consider separately the graph of .

Similarly with .

With , I think I would expect on a single graph a sketch showing (perhaps drawn as a broken line), and then an indication that shifts this graph 1 unit in the y-direction.

It would probably be too confusing to add to this same sketch, unless you used several colours. So, as a separate sketch, I should draw (lightly) , and again shift this 1 unit in the y-direction.

But that's only my opinion...

Grandad