Sine to Sine Squared Conversion - Historical First

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Sine to Sine Squared Conversion

In attempts to solve the elusive conversion, the key variables have been observed. The lesson for all of is to always consider an alternative variable, rather than many alternative iterations of the same few. Phase shift was the missing variable to consider. Then you can consider coefficients (1, 2 and 0.5) of the angle together with its its phase shift.

The example, below, will illustrate the difficulty of visually understanding the conversion. The formulas further down the page break past this obstruction.

(For confirmation of the the claim, please plot the two sets of graphs on any graph plotter which can also show you co-ordinates on the graph, to confirm co-alignment. Visual inspection is not sufficient.)

A   =   Sin ( x ) ,

A  = a * Sin^2 ( x / 2 + 5 * Pi / 4) - a;

A  =  Sin^2 ( x ) ,

A  =  ( a / 2 ) * Sin ( 2 * x + 3 * Pi / 2 ) + a/2

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