To graph this function on paper, its best to do this in steps....First graph six(x), then sin(x+pi)...which is a phase shift to the left by pi, then multiply by -1 (so the graph is rotated about the x axis), then vertical shift down by one.
amplitude= 1
period = 2 pi
phase shift is pi (to the left)
When you do a horizontal shift, you should look at it this way.....sin(x+pi)=sin(x - -pi), so the direction of the actual shift is second sign. If the function says y=-sin(x-pi)-1, then the phase (horizontal) shift would be sin(x - +pi), so the shift would be to the right.
