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Topic: How we get a Ellipse from a Conic, and how we get a Oval from
Cylinder Sections-- knifes that are V and asymmetrical V shaped

Replies: 27   Last Post: Oct 8, 2017 12:41 AM

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 Me Posts: 1,716 Registered: 1/23/16
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
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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

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