Introductory Trigonometry
Use sine, cosine and tangent to find missing sides and angles in right-angled triangles.
Overview
Trigonometry connects the angles and sides of a right-angled triangle through three ratios: sine, cosine and tangent. In Year 9 students meet these ratios for the first time and use them to find a missing side or angle. Trigonometry is one of the biggest IGCSE topics, so a confident start here pays off.
What You Will Learn
- Label the hypotenuse, opposite and adjacent sides relative to an angle
- Know the three ratios sin, cos and tan (SOH CAH TOA)
- Use a ratio to find a missing side in a right-angled triangle
- Use the inverse ratio to find a missing angle
- Choose the correct ratio for a given problem
Key Vocabulary
Common Mistakes to Avoid
- Labelling the opposite and adjacent sides the wrong way round for the angle
- Choosing the wrong ratio for the sides involved
- Forgetting to use the inverse (sin⁻¹, cos⁻¹, tan⁻¹) when finding an angle
- Having the calculator in the wrong angle mode (not degrees)
What Comes Next
At IGCSE this becomes the full Trigonometry topic, including angles of elevation and depression, bearings, and the sine and cosine rules.
Frequently Asked Questions
What does SOH CAH TOA mean?
It is a memory aid for the three ratios: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. You choose the ratio that uses the two sides involved in the question.
How do I find an angle with trigonometry?
Work out the ratio of the two known sides, then use the inverse function on your calculator. If tan of the angle is 0.5, the angle is tan⁻¹(0.5) ≈ 26.6°.
Study This Topic
Topic Details
- Stage
- Year 9
- Strand
- Geometry and Measure
- Framework ref
- 9Gg
- Difficulty
- High
Build strong foundations in Introductory Trigonometry
A free trial class with Teacher Rig helps your Year 9 child master Introductory Trigonometry now — so IGCSE Maths feels familiar, not frightening, later.
Heading toward IGCSE? See how Introductory Trigonometry develops in IGCSE Trigonometry (Cambridge 0580) →