One Triangle, Six Ratios | Class 11 · Trigonometry — Trigonometry Complete R1 | Namma Maths

One triangle. Six ratios. Zero memorised chants. This is Lesson 1 of Trigonometry Complete — and it starts the way every lesson in this series starts: with a picture. A ladder leans against a wall, five metres long, its foot three metres out. How high does it reach — and can you know without climbing? By the end of this lesson, you will answer that from a single 3-4-5 triangle. You will learn: • The three sides of a right-angled triangle — opposite, adjacent, hypotenuse — and how their names follow the angle you stand at • sin θ, cos θ, tan θ as honest comparisons of sides (3/5, 4/5, 3/4) • Why the ratios belong to the ANGLE, not the triangle's size • The three flips — cosec θ, sec θ, cot θ — and why flips multiply to 1 • The other angle: sin(90° − θ) = cos θ, and what "co-" really means • Your first exact answer: sin 45° = √2/2, derived, not memorised • The seed of everything: sin²θ + cos²θ = 1 📘 FREE NOTES for this lesson (printable PDF, with practice questions): https://drive.google.com/file/d/1jqhxvRC2-... CHAPTERS: 0:00 Hook — The Ladder Question 0:57 The Map — Twelve Lessons, One Circle 1:31 One Triangle — The Sides Get Names 3:07 Three Ratios — Sine, Cosine, Tangent 5:12 Any Size — Ratios Belong to the Angle 6:17 The Flips — Cosecant, Secant, Cotangent 7:42 The Other Angle — Complements (and the Ladder, Solved) 9:16 First Exact Answer — 45 Degrees 10:32 The Seed — sin²θ + cos²θ = 1 11:19 Your Turn — The 5-12-13 Triangle 12:16 Recap — One Triangle, Six Ratios 13:08 Summary Card 13:22 Next Time — Fundamental Identities NEXT: R2 — Fundamental Identities: Three Identities, One Circle. Trigonometry Complete playlist:    • Trigonometry Complete — Namma Maths   Music: "Frozen Star" by Kevin MacLeod (incompetech.com), licensed under CC BY 4.0.