This document describes how to rotate an ellipse by 45 degrees to the right. It defines the new angle after rotation as rot_theta, and provides formulas to calculate the new x and y coordinates (x = cos(rot_theta)*r_horizontal_ellipse, y = sin(rot_theta)*r_horizontal_ellipse) based on the original point's coordinates and the length of the straight line through the original point.

1. Rotated Ellipse: Part of the rotated sphere.
Sharon Liu.
2023/08/29.
Right upper quadrant: Both x and y are positive.

2. r_theta, is theta – 45. (Rotate 45 degrees, to the right.)
rot_theta, is the new angle.
r_horizontal_ellipse, is the length of the straight line.
r_horizontal_x, is the x-coordinate of the original point.
r_horizontal_y, is the y-coordinate of the original point.
cos(rot_theta) = x/r_horizontal_ellipse.
sin(rot_theta) = y/r_horizontal_ellipse.
x = cos(rot_theta)*r_horizontal_ellipse.
Y = sin(rot_theta)*r_horizontal_ellipse.
r_horizontal_ellipse = sqrt(r_horizontal_x^2 + r_horizontal_y^2).