Trigonometry (SOHCAHTOA)

When to use it

Right-angled triangles, to find a missing side OR angle (uses an angle).

Labelling the sides (relative to the angle)

• Hypotenuse (H) – longest, opposite the right angle
• Opposite (O) – opposite your chosen angle
• Adjacent (A) – next to your chosen angle

SOHCAHTOA

sin θ = O / H
cos θ = A / H
tan θ = O / A

Finding a side

Angle 30°, hypotenuse 10, find the opposite:

sin 30 = O / 10
O = 10 × sin 30 = 10 × 0.5 = 5

Finding an angle (use the inverse)

Opposite = 4, adjacent = 3:

tan θ = 4 / 3
θ = tan⁻¹(4/3) = 53.1°

Exact trig values to learn

θ	sin	cos	tan
0°	0	1	0
30°	1/2	√3/2	1/√3
45°	√2/2	√2/2	1
60°	√3/2	1/2	√3
90°	1	0	—

Non-right-angled triangles (higher)

• Sine rule: a/sin A = b/sin B = c/sin C
• Cosine rule: a² = b² + c² − 2bc·cos A
• Area = ½ ab sin C

Exam tip

Label H, O, A first, then pick the ratio using the two sides you know/want. To find an angle, use sin⁻¹ / cos⁻¹ / tan⁻¹.