While I'm not sure to be understanding what you are doing, I feel like you are not familiar with trigonometric graphs.

y = sin(x)

Is a curve starting at 0, going up to 1 at 90 degrees, goes back to 0 at 180 degrees, going further down till -1 at 270 degrees and up again to 0 at 360 degrees.

y =sin(x - Wolfram|Alpha)

Since you put the negative sign in front of the sine, you reflect the graph through the x-axis, giving:

y =-sin(x - Wolfram|Alpha)

Now, there is 1 in front. This means that you 'raise' the curve one unit up. Zeros thus become 1, 1s become 2s and -1s becomes 0s, like this:

y =-sin(x) +1 - Wolfram|Alpha
Now, if you can sketch such graphs on paper, knowing where the maxima, minima, and where the curve cuts the axes, you'll be better off finding the limits.

I hope it helped!