when y=-sinx and y=sin2x - sinx are added together and graphed, why do the maximum values of two sin functions occur where they do?
your new function is
y = (sin 2x - sinx) + sinx
= sin2x
notice your amplitude has not changed, so the maximum value is still 1.
your period is now 2pi/2 or 360º/2
= pi radians or 180º
If you look at the first complete graph, doesn't it reach its maximum at the end of the first quarter of its period?
And that would be pi/4 or 45º
check: what is sin (2*45º) ?