/sci/ - Science & Math

>>12332437
>>12332005
You can use the rotation matrix:
https://en.wikipedia.org/wiki/Rotation_matrix

For your transformation of [math]f(x) = \frac{1}{x}[/math] by an angle of 45 degrees CW, (god I hope the math shows up):
If we let [math]f(x) = \frac{1}{x} & F(x)[\math] be the rotated function, then
[math]F(x) = \left[ \matrix{\cos(-\frac{\pi}{2}) & -\sin(-\frac{\pi}{2}) \cr \sin(-\frac{\pi}{2}) & \cos(-\frac{\pi}{2})}\right] \cdot \left[ \matrix{x \cr \frac{1}{x}}\right] = \left[ \matrix{0 & 1 \cr -1 & 0}\right] \cdot \left[ \matrix{x \cr \frac{1}{x}}\right] = \frac{1}{x} - x[/math]
Hopefully this helps!