Grade 10 · CAPS-aligned
Grade 10 Trigonometry — Sin, Cos, Tan from Scratch
SOH-CAH-TOA, the special angles, and how to use trig in right-angled triangles.
Trig in Grade 10 is just three new buttons on your calculator and one mnemonic: SOH-CAH-TOA. Get those locked in this year and Grade 11 and 12 trig (identities, graphs, 2D/3D problems) becomes pattern-matching instead of guesswork.
Why most learners find this hard
Two things trip learners up: deciding which ratio to use, and the special angles. Spend a week drilling SOH-CAH-TOA on 20+ triangles and the rest follows.
What you'll learn
- Sin, cos, tan as ratios of sides in a right-angled triangle
- SOH-CAH-TOA — when to use which
- Exact values for 30°, 45°, 60° (no calculator)
- Solving for an unknown side and an unknown angle
- Angle of elevation and depression problems
Worked example
In a right-angled triangle, the opposite side is 7 and the hypotenuse is 14. Find the angle θ.
- 1Pick the ratio that uses opposite and hypotenuse: sin θ = opp / hyp
- 2Substitute: sin θ = 7 / 14 = 0.5
- 3Take the inverse: θ = sin⁻¹(0.5)
- 4From the special angles: θ = 30°
Answer: θ = 30°
Exam tips
- Mark which side is opposite and which is adjacent before picking a ratio.
- Learn the special angles cold — calculators are not allowed in some sections.
- Always check whether you should leave your answer to two decimals.
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