IGCSE Trigonometry
From SOH CAH TOA to the sine and cosine rules, with the exact point where each extension enters your tier.
What each tier expects
Core / Foundation
- • Label sides of right-angled triangles
- • sin, cos and tan of given angles
- • Find unknown sides and angles
- • Simple 3D right-angled triangles
Extended / Higher
- • Angles of elevation and depression
- • Bearings with measured diagrams
- • Sine rule and cosine rule
- • Area = ½ ab sin C
- • 3D problems with multiple steps
Not examined
- • Graphs of sin, cos and tan functions
- • Reciprocal and inverse ratios
- • Radians and the exact values beyond
- • standard angles (those begin at A-Level)
Knowing what is out of scope keeps revision focused.
Worked example: choosing the ratio
Find the height of the tower
Question. From a point 40 m from the base of a tower, the angle of elevation is 35°. Find the tower height, rounded to 1 decimal place.
Step 1. The height is opposite the angle, the ground distance is adjacent, so use tan: tan 35° = h / 40
Step 2. h = 40 × tan 35° = 40 × 0.7002… = 28.0 m (1 d.p.)
Exam tip: keep the full calculator value in memory and round only at the final line to avoid losing accuracy marks.
Sine rule: finding a side
Question. In triangle ABC, angle A = 48°, side a = 7 cm opposite angle A, and angle B = 62°. Find side b.
Step 1. a / sin A = b / sin B → 7 / sin 48° = b / sin 62°
Step 2. b = 7 × sin 62° / sin 48° = 8.4 cm (1 d.p.)
Use the sine rule when you have a matching angle-and-opposite-side pair; use the cosine rule when you have two sides and the angle between them, or all three sides.
Common traps
- ×Pressing sin on the calculator before typing the angle: always enter the angle first, then apply the inverse function.
- ×Bearings measured anticlockwise or not to three digits. The convention is clockwise from north, always three figures.
- ×Mixing degrees and radians on the calculator. Check the mode indicator before every paper.
- ×Rounding mid-question. Carry the unrounded value through every step and round once at the end.
More IGCSE guides
IGCSE Algebra →
Equations, identities, sequences, graphs and the algebra skills both syllabi assess most
IGCSE Geometry →
Shapes, mensuration, transformations and vectors, from Core basics to Extended proofs
IGCSE Statistics & Probability →
Averages, charts, cumulative frequency, histograms and probability, including set notation
IGCSE Maths Revision Plan →
A term-by-term revision timetable that adapts to Core, Extended, Foundation or Higher entry
IGCSE Past Papers →
Where to find official past papers and how to turn them into a marking-backed study loop
IGCSE Grade Boundaries →
How raw marks become grades, why boundaries move each series, and how to read official documents
IGCSE vs O-Level →
Recognition, syllabus and entry differences between IGCSE and GCE O-Levels
IGCSE Math Tuition →
What to evaluate in an IGCSE maths tutor, and how adaptive practice compares
← Back to the IGCSE Math hub
Syllabus comparison, tier decisions and grade guides in one place
Want ReLURN for IGCSE?
ReLURN today covers Singapore MOE from PSLE to O-Level. IGCSE is the next curriculum our students ask for most. Add your email and we will notify you the moment IGCSE practice goes live.
One launch email. No spam. Unsubscribe anytime.