Appendix A · Study sheet
Trigonometry
Pointer: trigonometry.tex. This is a crib sheet, not the appendix.
You need the unit circle more than you need identities trivia. \(\cos\theta\) and \(\sin\theta\) are the coordinates of a heading. Adjacent and opposite are what you name after you draw the triangle in the robot’s current frame. If a sign is wrong, redraw; do not flip symbols until it “looks right.”
Keep these in muscle memory: \(\cos^2+\sin^2=1\); the angle-addition formulas when you stack two headings; \(\text{atan2}(y,x)\) instead of \(\arctan(y/x)\) so the quadrant survives. Small-angle: \(\sin\theta\approx\theta\), \(\cos\theta\approx 1-\theta^2/2\) with \(\theta\) in radians. That last line is how Jacobians stay pretty in Part IV.
\(\text{atan2}(y,x)\) returns \(\theta\in(-\pi,\pi]\). Wrapping: never subtract headings without wrapping to that interval.