IGCSE Maths 0580 · Common mistakes
Common trigonometry mistakes in IGCSE Maths
Updated · by the Fahmazing team
Trigonometry questions are worth several marks each, and one wrong choice at the start loses the lot. Most errors come from labelling the sides wrongly or from calculator slips. Here is how to avoid them.
1. Mixing up the adjacent and the hypotenuse
Both sides touch the angle, but the hypotenuse is always the longest side, opposite the right angle. Label O, A and H before you choose sin, cos or tan.
- Opposite and hypotenuse: sin.
- Adjacent and hypotenuse: cos.
- Opposite and adjacent (no hypotenuse): tan.
Free lesson: Right-angled triangles
2. Dividing when you should multiply (and the other way round)
If the unknown is on top of the fraction, multiply. If it is on the bottom, divide.
The hypotenuse is 10 cm and the angle is 35°. Find the opposite side.
✗ Wrong: O = 10 ÷ sin 35° = 17.4 cm (longer than the hypotenuse: impossible)
✓ Right: sin 35° = O ÷ 10, so O = 10 × sin 35° = 5.74 cm
Free lesson: Right-angled triangles
3. Forgetting the inverse to find an angle
To go from a ratio back to an angle, use sin⁻¹, cos⁻¹ or tan⁻¹ (shift then the trig key).
The opposite side is 5 cm and the adjacent side is 8 cm. Find the angle.
✗ Wrong: tan θ = 5 ÷ 8 = 0.625, so θ = 0.625
✓ Right: θ = tan⁻¹(0.625) = 32.0° (1 d.p.)
Free lesson: Right-angled triangles
4. Calculator in radians
Your calculator must be in degrees mode (a small D on the screen). In radians mode every answer is wrong, sometimes even negative.
Work out 10 × sin 35°
✗ Wrong: Radians mode: −4.28
✓ Right: Degrees mode: 5.74
Free lessons: Using a calculator · Right-angled triangles
5. The cosine rule: subtracting before multiplying
In a² = b² + c² − 2bc cos A, the cos A multiplies only the 2bc part. Then remember the square root at the end.
b = 7 cm, c = 9 cm, A = 50°. Find a.
✗ Wrong: (49 + 81 − 126) × cos 50° = 2.57, so a = 1.60 cm
✓ Right: a² = 49 + 81 − 126 × cos 50° = 130 − 80.99 = 49.01, so a = 7.00 cm (3 s.f.)
Free lesson: Non-right-angled triangles
6. Using ½ × base × height when the triangle has no right angle
Two sides with the angle between them need the formula area = ½ab sin C.
Two sides are 7 cm and 9 cm with an angle of 50° between them. Find the area.
✗ Wrong: ½ × 7 × 9 = 31.5 cm²
✓ Right: ½ × 7 × 9 × sin 50° = 24.1 cm² (3 s.f.)
Free lesson: Non-right-angled triangles
7. Choosing the wrong rule
- Two angles and a side, or a side-angle pair plus one more: sine rule.
- Two sides and the angle between them, or all three sides: cosine rule.
- After the sine rule for an angle, press sin⁻¹. If sin B = 0.514, then B = 30.9°, not 0.514.
Free lesson: Non-right-angled triangles
Questions students ask
How do I know whether to use sin, cos or tan?
Label the sides opposite, adjacent and hypotenuse from the angle. Write down the two sides you know or want, then match them: O and H is sin, A and H is cos, O and A is tan.
When do I use the sine rule or the cosine rule?
Use the cosine rule when you know two sides and the angle between them, or all three sides. Otherwise, when you know a side and its opposite angle, use the sine rule.
How accurate should trigonometry answers be?
Give lengths to 3 significant figures and angles to 1 decimal place, unless the question says otherwise. Keep full calculator values until the end.