Trigonometry Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about trigonometry for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Right-Angled Triangle Trigonometry (SOH CAH TOA)
The three basic trigonometric ratios relate the sides of a right-angled triangle to its angles. Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tan = Opposite/Adjacent. Remember: the hypotenuse is always the longest side, opposite the right angle. The opposite side is across from the angle you are working with, and the adjacent side is next to it (but not the hypotenuse).
Key Formulas
- sin A = opposite / hypotenuse
- cos A = adjacent / hypotenuse
- tan A = opposite / adjacent
Exam Tips
- Always label O, A, H relative to the angle you are using
- Check your calculator is in degree mode
- If given two sides, you can find any angle using the inverse function
The Sine Rule
The sine rule is used in non-right-angled triangles when you have a matching pair (a side and its opposite angle). It states that in any triangle, the ratio of a side to the sine of its opposite angle is constant. Use it when you know: (1) two angles and one side (AAS), or (2) two sides and a non-included angle (SSA, but beware the ambiguous case).
Key Formulas
- a/sin A = b/sin B = c/sin C
- sin A/a = sin B/b = sin C/c (use this form when finding angles)
Exam Tips
- Use the first form when finding sides, the second when finding angles
- The ambiguous case occurs with SSA - check if the obtuse angle solution is also valid
- You need at least one complete opposite pair to start
The Cosine Rule
The cosine rule is used when you have: (1) two sides and the included angle (SAS) to find the third side, or (2) all three sides (SSS) to find an angle. It is an extension of Pythagoras that works for any triangle.
Key Formulas
- a squared = b squared + c squared - 2bc cos A
- cos A = (b squared + c squared - a squared) / (2bc)
Exam Tips
- Use the first form to find a side, the second to find an angle
- When cos A is negative, angle A is obtuse (greater than 90 degrees)
- Always use the cosine rule before the sine rule if you have SAS or SSS
Area of a Triangle
When you know two sides and the included angle, you can find the area without needing the height. This formula is especially useful in non-right-angled triangles.
Key Formulas
- Area = (1/2)ab sin C
Exam Tips
- The angle must be BETWEEN the two sides you are using
- This formula is on the formula sheet but you should know how to use it quickly
- Combine with the sine/cosine rule in multi-step problems
Bearings and Trigonometry
Bearings are measured clockwise from North and always written as three figures (e.g., 045 degrees, not 45 degrees). Many bearing problems require the sine rule, cosine rule, or basic trigonometry. Always draw a clear diagram with North lines at every relevant point.
Key Formulas
- Back bearing = bearing +/- 180 degrees
Exam Tips
- Always draw a North line at every point in your diagram
- The angle in your triangle is found from the bearings, often by using angles on a straight line or co-interior angles
- Bearing questions are worth many marks - draw large, clear diagrams
Revision Checklist
- I understand all key concepts in trigonometry
- I have memorised the essential trigonometry formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on trigonometry
- I know the common mistakes to avoid in trigonometry questions
Frequently Asked Questions
What trigonometry topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers trigonometry across both Core and Extended tiers. Key areas include right-angled triangle trigonometry (soh cah toa). Key areas include the sine rule. Key areas include the cosine rule.
How important is trigonometry in the IGCSE exam?
Trigonometry is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine trigonometry with other topics.
What are the most common mistakes in trigonometry?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For trigonometry specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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