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Whilst doing a Geometry problem, I formed this function which inputs angle X and outputs angle Y. I currently have it written as follows;

[math]f(x)=\arcsin{\frac{\cos{2x}-\sin{2x}}{\sqrt{2}}}[/math]

No code has to be inserted here.

The plot of this graph looks like this.

Having never been taught functions, I am a bit naive about whether or not this function is special, or what type of function it even is. I can tell from the table that as X increases, Y decreases until a point (where X is 22.5 degrees), at which point Y begins to increase along with X. I also know that, since it was derived from a geometry problem involving acute angles, X and Y cannot pass above 45 (since twice that is 90). Since, again, they are angles, X and Y are also limited to a lower limit of zero. Given this information, is anyone willing to help me find out more about this function? Any other ways to write it, what it tells me about the angles?

Pardon any ignorance in the above post, as I am working off of only what I have taught myself about functions, so some of it may not make sense.

[math]f(x)=\arcsin{\frac{\cos{2x}-\sin{2x}}{\sqrt{2}}}[/math]

No code has to be inserted here.

The plot of this graph looks like this.

Having never been taught functions, I am a bit naive about whether or not this function is special, or what type of function it even is. I can tell from the table that as X increases, Y decreases until a point (where X is 22.5 degrees), at which point Y begins to increase along with X. I also know that, since it was derived from a geometry problem involving acute angles, X and Y cannot pass above 45 (since twice that is 90). Since, again, they are angles, X and Y are also limited to a lower limit of zero. Given this information, is anyone willing to help me find out more about this function? Any other ways to write it, what it tells me about the angles?

Pardon any ignorance in the above post, as I am working off of only what I have taught myself about functions, so some of it may not make sense.

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