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Play With Trigonometry

Grab the angle. Watch the maths react.

Every trigonometry idea from Classes 9–10, turned into a toy. Drag, scale, snap and fold — no marks, no mastery score, just you and a responsive triangle. Read the research behind it.

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All 52 Play With Trigonometry lessons

Every lesson in the series, by class. Every lesson is free to play once you sign in.

Class 9

  • Pick Your Angle, Name Your Sides — Perpendicular and base swap the moment you change the reference angle. · Trigonometrical Ratios
  • θ, φ, α — the Angle Alphabet — Trigonometry names its angles with Greek letters. Say them as you set them. · Trigonometrical Ratios
  • Six Ratios, Three Sides — sin, cos, tan — and their three reciprocals. All from one triangle. · Trigonometrical Ratios
  • The Ratio That Won't Budge — Scale the triangle — watch the sine stay exactly where it is. · Trigonometrical Ratios
  • The 5-12-13 Detective — Two sides known, Pythagoras finds the third — then every ratio falls out. · Trigonometrical Ratios
  • One Ratio Unlocks All — Know cot A = 4/3? Then you know everything — the k-method. · Trigonometrical Ratios
  • The Flip Side — cosec, sec and cot are just sin, cos and tan upside-down. · Trigonometrical Ratios
  • tan Is Just sin ÷ cos — Watch the division happen live — the hypotenuse cancels out. · Trigonometrical Ratios
  • Rhombus, Meet Trigonometry — cos α = 0.8 cracks a whole rhombus — diagonals, side, perimeter. · Trigonometrical Ratios
  • Half an Equilateral — Fold a 2a-sided equilateral triangle — out fall the exact values for 30° and 60°. · Trigonometrical Ratios of Standard Angles
  • The Square's Diagonal — Cut a square corner-to-corner: legs a and a, hypotenuse √2·a. · Trigonometrical Ratios of Standard Angles
  • The Table, Live — 0-30-45-60-90: sin climbs 0→1, cos slides 1→0. Watch them race. · Trigonometrical Ratios of Standard Angles
  • The Sum That's Always 1 — sin²θ + cos²θ = 1 at every single angle. Try to break it. · Trigonometrical Ratios of Standard Angles
  • The Trap: sin(A+B) ≠ sin A + sin B — The most common trig mistake on any board paper — watch it fail. · Trigonometrical Ratios of Standard Angles
  • Exact Values, No Calculator — sin²30° − 2cos³60° + 3tan⁴45° — melt it down with the table. · Trigonometrical Ratios of Standard Angles
  • Hunt the Angle — sin 2A = 1. Which A makes it true? Unwind it. · Trigonometrical Ratios of Standard Angles
  • Formula Stress-Test — cos 3A = 4cos³A − 3cosA. Don't trust it — test it at A = 30°. · Trigonometrical Ratios of Standard Angles
  • Two Clues Solve Everything — One side + one angle (or two sides) — the whole triangle surrenders. · Solution of Right Triangles
  • Pick the Right Ratio — unknown/known = the ratio of the given angle. Choose so the unknown sits on top. · Solution of Right Triangles
  • Reverse Gear — The ratio is 5/10. Which angle made it? · Solution of Right Triangles
  • Two Triangles, One Secret Side — 45° here, 30° there, sharing one height — eliminate it. · Solution of Right Triangles
  • The Trapezium Job — ∠C = 120° up top forces ∠B = 60° at the base (co-interior angles) — drop a perpendicular and harvest. · Solution of Right Triangles
  • Rocket, Ladder, Kite — Three stories, one triangle. 40 km at 60° to the vertical — how high is the rocket? · Solution of Right Triangles
  • Locked at 90° — Two acute angles, one right-angle budget. Spend it between them. · Complementary Angles
  • The Fold That Renames Sine — Fold θ onto 90° − θ — sin becomes cos before your eyes. · Complementary Angles
  • tan ↔ cot — Same fold, next pair: tan θ = cot(90° − θ). · Complementary Angles
  • sec ↔ cosec — Third pair folds too: sec θ = cosec(90° − θ). Collect the full set. · Complementary Angles
  • The Great Collapse — cos 47°/sin 43° looks scary — one fold and it's just 1. · Complementary Angles
  • Half-Angles in Hiding — A + B + C = 180° hides a complement: (A+B)/2 and C/2. · Complementary Angles
  • Undo the Disguise — cos 38° · sec(90° − 2A) = 1 — strip the co-functions, find A. · Complementary Angles

Class 10

  • Warm-Up: Ratios Don't Rust — Three quick drills — one reciprocal, one quotient, one Pythagorean — before the real proofs begin. · Trigonometrical Identities
  • Pythagoras, Divided Three Ways — One theorem ÷ AC², AB², BC² = three identities. · Trigonometrical Identities
  • True Everywhere, or True Once? — sin²θ + cos²θ = 1 vs sin θ = ½ — only one survives every angle. · Trigonometrical Identities
  • The Eight-Identity Toolkit — Three reciprocal, two quotient, three Pythagorean — every proof in 11th and 12th starts here. · Trigonometrical Identities
  • Rearrange the Squares — sin²A = 1 − cos²A · tan²A = sec²A − 1 · cot²A = cosec²A − 1 — the three moves every proof uses. · Trigonometrical Identities
  • Start with the Harder Side — tan A + cot A → sec A · cosec A, in slides and fuses. · Trigonometrical Identities
  • The Difference-of-Squares Move — cos⁴A − sin⁴A = 2cos²A − 1 = 1 − 2sin²A — the pattern that becomes cos 2A next year. · Trigonometrical Identities
  • Partner Pairs — (sec A − tan A)(sec A + tan A) = 1 — each is the other's reciprocal. Same for cosec ± cot. · Trigonometrical Identities
  • The Conjugate Trick — A square root that hides sec A − tan A — multiply by the conjugate to free it. · Trigonometrical Identities
  • Add the Fractions — sin A/(1 + cos A) + (1 + cos A)/sin A = 2 cosec A — common denominator, then the toolkit. · Trigonometrical Identities
  • Introduce p — sec A + tan A = p → sin A = (p² − 1)/(p² + 1) — identities turned into algebra. · Trigonometrical Identities
  • Make the Angle Vanish — x = a·secA·cosB, y = b·secA·sinB, z = c·tanA — combine until A and B are gone. · Trigonometrical Identities
  • Co-functions in the Forge — tan 10° · tan 15° · tan 75° · tan 80° — pair them off to 1. · Trigonometrical Identities
  • Between the Famous Angles — sin 36°51′ isn't on any exam table you memorised — dial it anyway. · Trigonometrical Identities
  • Up-Angles and Down-Angles — Line of sight vs the horizontal — and why the two angles always match. · Heights and Distances
  • Race the Shadow — Shadow √3 times the height? The sun sits at exactly 30°. · Heights and Distances
  • Every Tower Is a Triangle — Tower, ladder, broken tree — different costume, same right triangle. · Heights and Distances
  • Walk Closer, Angle Climbs — Two viewpoints, two equations, one tower — subtract and solve. · Heights and Distances
  • The Car's Countdown — Depression 30° → 45° in 12 minutes. When does the car arrive? · Heights and Distances
  • The Cloud in the Lake — Elevation 30° to the cloud, depression 60° to its reflection — height falls out. · Heights and Distances
  • From the Pole Top — Look up 60° to the tower's top, down 30° to its foot — the tower is 80 m. · Heights and Distances
  • The Lighthouse Keeper — Midnight, 180 m up. A boat radios: "how far out are we?" — you answer with a table. · Heights and Distances
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