Finding highest value of curve

Question

I have the question "The instantaneous values of two alternating voltages are given by v1 = 5sinwt and v2 = 8sin(wt - pi/6). By plotting v1 and v2 on the same axes, using the same scale, over one cycle, obtain expressions for v1 + v2."

Here is the data for the graph which I have worked out:

The highest/Max value here is 11.9, however the solutions say that the expression should be:

v1 + v2 = 12.6sin(wt - 0.32) V,

Here I can see that the maximum should be 12.6 and not 11.9 so where have I gone wrong ?

Answer 1

Plotting the graph between 90 degrees and 135 degrees at intervals of 5 degrees you will get a higher value nearer to the solution.Else for best accuracy you can combine them ( same frequency) and phase shift.