Rotation of curve function

Question

I am working on some coding where I require expertise in field of Mathematics. I have a function:

$$F(x) = -0.007x^4 + 1.971x^3 - 190.4x^2 + 8150x - 13024$$

I want to rotate some section of this function (i.e. part of the function where $65 < x < 75$) about a point at $x = 65$ to certain angle lets say $\theta$. Rotating the function at $x= 65$ is important.

Answer 1

What you want is quite complicated.

Maybe easiest is to plot your new curve:

• Transform the whole curve into a parameter curve first so instead if $y = f(x) $ use

$ y = f(t)$ and $x = g(t) $ instead, (in your case $g(t) $ is just $t$ )

• Then to rotate around point $A(A_x,A_y)$ by angle $\varphi$ you get:

$x_r = A_x + (g(t) - A_x) \cos(\varphi) - (f(t) - A_y) \sin(\varphi) $

$y_r = A_y + (g(t) - A_x) \sin(\varphi) + (f(t) - A_y) \cos(\varphi) $

• Connect the consecutive points $(x_r , y_r)$

GOOD LUCK