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'At the stroke of midnight, your brother will be hurtling sideways at an altitude of 150 meters' is a regular physics prediction about your nonmagical trebuchet, whereas 'you are cursed to build a brother-launching trebuchet' falls out of the Lagrangian.
Imagine taking a line and rolling it around a circle so that it's always touching. Like a wheel on a flat surface, but from the wheel's perspective.
Sine and cosine are the X and Y coordinates of the intersection point, and tangent is the slope of the line.
You can also relate it back to acoustics!
Woah