Learn the basics step by step — with a full cheat sheet and 20 easy practice questions!
📐 Step 1 — The Right Triangle
3 sides to remember:
Hypotenuse (H) The LONGEST side. Always opposite the right angle (90°).
Opposite (O) The side ACROSS from angle θ.
Adjacent (A) The side NEXT TO angle θ (not the hypotenuse).
🔑 Step 2 — The Magic Word: SOHCAHTOA
⚡ #1 Most Important Memory Key in Trigonometry
SOH · CAH · TOA
Sin = Opposite ÷ Hypotenuse SOH
Cos = Adjacent ÷ Hypotenuse CAH
Tan = Opposite ÷ Adjacent TOA
📋 Step 3 — 4 Key Formulas
🟣
sin θ
O ÷ H
Opposite ÷ Hypotenuse ▸ SOH
🔵
cos θ
A ÷ H
Adjacent ÷ Hypotenuse ▸ CAH
🟠
tan θ
O ÷ A
Opposite ÷ Adjacent ▸ TOA
🟢
Pythagoras
a² + b² = c²
c = hypotenuse a, b = two legs ▸ a²+b²=c²
⭐ Step 4 — Special Angles (Memorize These!)
Angle
sin θ
cos θ
tan θ
0°
0
1
0
30°
1/2
√3/2
1/√3
45°
1/√2
1/√2
1
60°
√3/2
1/2
√3
90°
1
0
❌ undefined
💡
Easy way to remember sin values: sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.
They just keep getting bigger as the angle gets bigger! 📈
And cos is the opposite — it gets smaller as the angle gets bigger! 📉
🏆 Step 5 — Pythagorean Triples (Must Know!)
🥇
3 – 4 – 5
3²+4²=5² 9+16=25 ✓
🥈
5 – 12 – 13
5²+12²=13² 25+144=169 ✓
🥉
6 – 8 – 10
3-4-5 × 2 (scaled triple)
🎯
Big Secret! 6-8-10 is just 3-4-5 multiplied by 2.
You can always scale a triple! Try: 3-4-5 × 3 = 9-12-15. Also a triple! 🤯