By hand, it's actually very easy. The sin function oscillates between 0 at x=pi and 1 at x=0.5pi. The 1/2 in front of the sin function means the amplitude is half as tall as it would be, so the max height is 0.5

At x=0, y=0

At x=0.5pi, y=-0.5

At x=pi, y=0

At x=3/4pi, y=0.5

At x=2pi, y=0

And there you have it!

May 14th, 2015

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