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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

A typical sine wave will shink by 2 in x and y dimensions if squared.

See diagram.

But if the sine wave was a certain amplitude before it was squared it

would get bigger.

So there should exist an amplitude of a sine wave that when squared,

stays the same amplitude.

However, the wavelength will always continue to be halved.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

Oh yes, an amplitude of 2 which is a sine wave that varies from 2 to -2 in its height.

The two will square to 4, and the negative part of the wave will become positive, so the amplitude will be 2 again because it varies from 0 to 4 now, instead of -2 to 2.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,552

Also if you square a sine or cosine wave that is shifted up or down any amount, then the resulting shape is no longer a sine or cosine wave shape, it is misshapen. I plotted a lot of examples to see this.

Also, the power reduction formula for sine and cosine say that the square of a sinewave is still a sinewave, but shifted in x and y, and half the size.

One source says: (sin x)^2 = (1 - cos (2x))/2

**igloo** **myrtilles** **fourmis**

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**krassi_holmz****Real Member**- Registered: 2005-12-02
- Posts: 1,908

, which is TRUE

IPBLE: Increasing Performance By Lowering Expectations.

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