Trigonometric relationships (internal)
Internal 3 credits Sine rule Cosine rule Area Ambiguous case Radians SectorsAS 91259, 3 credits. Non-right-angled triangles via the sine and cosine rules, triangle area, arcs and sectors, and often a 3-D or bearings problem. Almost always set in a real measuring context — surveying, navigation, construction.
1 Reading the notation
A closed list of five method areas — arc length, sector area, and the two triangle rules.📖 Terms the schedule grades you on
2 terms- Apply methods (Achieved)
- Select and use methods; demonstrate knowledge of trigonometric concepts and terms; communicate using appropriate representations.
- Named methods (note 4)
- Arc length, sector area, sine rule, cosine rule, area of a triangle.
2 What the grades require
The same ladder every L2 maths internal uses.| Grade | What it takes | The half people drop |
|---|---|---|
| Achieved | Select and use methods; know the concepts and terms; communicate with appropriate representations | Showing no working — the method IS the evidence |
| Merit | A logical sequence of steps, connecting concepts, or forming and using a model | The "and also": relate findings back to the context |
| Excellence | Devise a strategy, build a chain of reasoning or a proof, or form a generalisation | The "and also": correct mathematical statements, or a stated insight |
Both Merit and Excellence are "one or more of … AND ALSO …". A perfect answer that never interprets its result in context cannot pass the Achieved ceiling.
3 Choosing the right rule
What you are given decides the tool.| Given | Use | Watch for |
|---|---|---|
| Two angles + any side (AAS) | Sine rule | Third angle = 180° − the other two |
| Two sides + non-included angle (SSA) | Sine rule | THE AMBIGUOUS CASE — check both |
| Two sides + included angle (SAS) | Cosine rule | Then sine rule for the rest |
| Three sides (SSS) | Cosine rule rearranged | Find the largest angle first |
| Two sides + included angle, area wanted | Area = ½ab·sin C | The angle must be INCLUDED |
Sketch the triangle and label what you know before choosing. Most wrong-rule errors are visible in the sketch.
4 Arcs and sectors
Radian forms are cleaner — check the calculator mode every time. ✕Degree/radian mismatch
A calculator left in the wrong mode produces a plausible-looking wrong answer with no error message. Before any trig calculation, check the mode matches what the problem is set in.5 3-D problems and bearings
Break the solid into flat triangles, solved in sequence.The 3-D strategy
- Identify each triangle in the solid.
- Redraw each one flat, in 2-D, with its known values.
- Solve in the order where one triangle's answer feeds the next.
- State which order you used, and why — that reasoning is part of the mark.
Practice
Recall it first, then use it — testing yourself builds the memory, where rereading the notes above only feels easier.
Recall and application shuffled together — you have to work out what each item wants before you can answer it, which is the part the exam actually tests. Both kinds feed the same spacing schedule, so anything you miss comes back sooner.
Say the answer out loud before flipping — that attempt is where the learning happens, even when you get it wrong.
Exam-style only. Instant feedback, shuffled each attempt, best score saved on this device.