A precise definition
Trigonometry is the branch of mathematics that studies the relationships between the angles and sides of triangles — specifically the six ratios (sine, cosine, tangent and their reciprocals) that connect an angle to the proportions of a right-angled triangle. But that is only where it starts. Extend those ratios to all angles and you get wave functions. Use wave functions and you can describe sound, light, electricity, tides, seasons, and the orbit of every planet. Trigonometry is how mathematics talks about anything that repeats.
The problem it was invented to solve
The ancient Egyptians built the pyramids with empirical knowledge of triangular ratios. Greek astronomers — particularly Hipparchus around 150 BC — needed to calculate the positions of stars and planets precisely, which forced them to formalise the relationships between angles and chord lengths. Indian mathematicians (Aryabhata, 6th century) introduced the sine function we use today. The name comes from Arabic: "jiba" (chord) was mistranslated as "jaib" (pocket/bay) and rendered into Latin as "sinus." Every time you write sin(x) you are tracing a 1,400-year chain of mathematical translation.
Where you find it in the world — including South Africa
These are not contrived textbook examples. Each application below is currently in use, driven by real institutions, and producing real outcomes.
Cell tower placement — MTN, Vodacom, and every SA network
Every base station in South Africa is positioned using trigonometric calculations. Engineers use bearing angles, elevation angles, and signal propagation models (all built on sine and cosine) to maximise coverage while minimising interference. The 60,000+ cell towers across SA are a trigonometry problem at scale.
GPS and satellite navigation
Your phone receives signals from multiple satellites simultaneously. Triangulating your position from those signals requires solving systems of trigonometric equations in real time. Without trigonometry, GPS accuracy degrades from metres to kilometres.
Bridge and tunnel engineering
The Gautrain's underground tunnels required precise angular calculations to ensure segments meet correctly deep underground. Every suspension bridge — including the iconic bridges in Cape Town's Boulders Beach area and the N2 over the Gamtoos River — is designed using trigonometric force analysis.
Sound engineering and music production
Sound is a pressure wave. Microphones, speakers, equalisers, and digital audio formats (MP3, AAC) all use Fourier analysis — which decomposes any sound into trigonometric sine waves. South African studios producing Amapiano or Afrobeats are running trig thousands of times per second.
DStv satellite dish alignment
Every DStv dish must be aimed at a specific satellite 35,786 km above the equator. The azimuth and elevation angles that determine dish position are pure trigonometry, calculated from your GPS coordinates.
Medical imaging — MRI and CT scans
MRI machines reconstruct images from radiofrequency signals using an algorithm called the Fourier Transform — which is trigonometry extended to continuous functions. Every scan taken at Groote Schuur or Charlotte Maxeke hospital is a trigonometric reconstruction.
You've already encountered this
You have already used trigonometry without knowing it. When you read a map bearing, adjust a satellite dish, or watch how shadows lengthen at sunset, you are observing trigonometric relationships. The fact that a 1-degree error in a long-range rifle shot causes a miss of 17 metres at 1 km is a trigonometric consequence.
What you study — and when
- ›Right-angled triangles: sin, cos, tan definitions and the CAST diagram
- ›General angles: extending trig to all four quadrants
- ›Trig identities: Pythagorean identity, compound angle formulas
- ›Solving trig equations: finding all solutions in a given interval
- ›3D trigonometry: applying trig to real three-dimensional problems
- ›Trig graphs: transformations of sin(x), cos(x), and tan(x)
Related topics and institutions
Trigonometry in CAPS is the gateway to 6 university-level disciplines.
The Continuum teaches you the CAPS trigonometry curriculum with the depth and context that makes the applications above feel obvious — not abstract. Start with the foundation that opens every door above.
No card required. South African curriculum. Grade 8–12.