🎓 Deeper Dive — Adults

For a right triangle with angle θ: sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj. Mnemonic: SOH CAH TOA.

Pythagorean identity: sin²θ + cos²θ = 1 (true for all θ).

Standard values: sin 30° = 1/2, cos 30° = √3/2, sin 45° = cos 45° = 1/√2, sin 60° = √3/2.

Trig extends to all real angles via the unit circle, generating periodic sin/cos waves used everywhere in physics and signal processing.