Trigonometry (SOH CAH TOA)
Year 9 📐 Geometry & Measures Use sin, cos and tan to find missing sides and angles.
📐 SOH CAH TOA
Trigonometry uses ratios of sides in right-angled triangles.
⚡ The Three Ratios
$$\sin\theta = \frac{\text{Opposite}}{\text{Hypotenuse}} \qquad \cos\theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} \qquad \tan\theta = \frac{\text{Opposite}}{\text{Adjacent}}$$ SOH-CAH-TOA — Some Old Hens Cackle And Howl Till Old Age!
🔢 Common Angles
| θ | sin θ | cos θ | tan θ |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | ½ | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | ½ | √3 |
| 90° | 1 | 0 | undefined |
🔎 Finding Angles & Sides
Find angle: If $\sin\theta = 0.5$ then $\theta = \sin^{-1}(0.5) = 30°$
Find side: Opposite = hyp × sin(θ) = 10 × sin(40°) ≈ 6.43
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Interactive Demonstration — Trigonometry (SOH CAH TOA)
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📐 Trigonometry Calculator
Triangle Solver (right-angled triangle)