Let's first graph y = sin 2x (without the "+ 1") to get an idea of what phase shift means.

The amplitude is 1 and the period is 2π/2 = π.

I have drawn a little more than 2 cycles, starting from x = 0.

Now let's consider the phase shift. Using the formula above, we will need to shift our curve by:

This means we have to shift the curve to the left (because the phase shift is negative) by 0.5. Here is the answer (in blue). I have kept the original y = sin 2x (in dotted gray) so you can see what's happening.

Note that the curve passes through:

• (-0.5, 0) on the x-axis (because we shifted the curve to the left by 0.5) and
• sin 1 = 0.84 on the y-axis. This figure is obtained by substituting x = 0 into y = sin(2x + 1); (in radians, of course).