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Re: 11) Is Andrew Wiles, John Conway failures of trigonometry like Burse//sine wave is semicircle Not sinusoidal
Posted:
Oct 7, 2017 5:16 PM


On Saturday, October 7, 2017 at 2:54:00 AM UTC+2, Archimedes Plutonium wrote:
> Thus making the sine graph and cosine graph to be a SEMICIRCLE graph.
Look, Archie, this CANNOT be the case.
Proof:
Let's assume that you were right.
Then (x  1)^2 + sin^2(x) = 1 and hence sin^2(x) = 1  (x  1)^2 .
And x^2 + cos^2(x) = 1, hence cos^2(x) = 1  x^2 .
The two semicircles would intersect at a point x such that sin^2(x) = cos^2(x), hence 1  x^2 = 1  (x  1)^2, hence x^2  2x + 1 = x^2, hence 1  2x = 0, hence x = 1/2.
But then, for this x, we would have
sin^2(x) + cos^2(x) = sin^2(1/2) + cos^2(1/2) = 2 * 3/4 = 3/2 = 1.5
Now from Pythagoras and the definition of sin and cos we have sin^2(x) + cos^2(x) = 1 for all x. Contradiction!
qed
See: https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity

