You calculate y = sin 2x for various values of "x", plot the points in the diagram, and join the points.
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It is a graphs which is similar to that of sin(x) but with the horizontal changes reduced to half as much.
d/dx (sin x + sin 2x) = cos x + 2cos 2x
0. sin 2x = cos 3x 1. sin 2x = sin (pi/2 - 3x) [because cos u = sin (pi/2 - u)] 2. [...]
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It is 9.1 inches (approx). L*[sin(x) + sin(2x) + sin(3x) +sin(4x)] = 28 inches where x = 360/10 = 36 degrees. Since x = 36 deg, sin(x) = sin(4x) and sin(2x) = sin(3x) So L*[2sin(x) + 2sin(2x)] = 28 inches L*[sin(x) + sin(2x)] = 14 inches L* 1.539 = 14 approx so that L = 9.098 inches or 9.1 inches, approx.
cos(2x) = 1 - 2(sin(x)^2), so sin(x)^2 = 1/2 - 1/2*cos(2x).