Trigonometry

Half a square and half an equilateral: the two triangles behind every exact value of 30°, 45°, and 60°.

Angles measured by arc, a circle where cosine and sine ARE the coordinates — and exact values in every quadrant.

The circle unrolled into a wave: amplitude, period, phase, midline — and tangent's wilder portrait.

The Pythagorean identity, sum and double-angle formulas — and solving equations whose unknown is an angle.

Trigonometry for EVERY triangle: the sine area formula, both laws, and the strategy for solving any triangle from any three facts.