Trigonometry
MYP Year 5 Extended Mathematics — Trigonometry unit (MYP has no numbered subject-guide codes; referenced here by unit name only)
Right-triangle trig (SOH CAH TOA) only ever worked because you had a angle to lean on. The moment a triangle stops being right-angled — which is most real triangles, most land plots, most bearings problems — you need a different toolkit: the sine rule, the cosine rule, and the trig area formula. This chapter is really about one decision: given the information in front of you, which of the three tools actually applies? Get that decision right and the arithmetic is routine; get it wrong and you'll substitute into a formula that can't use the data you were given.
Overview
Why right-angle trig stops being enough
SOH CAH TOA needs a angle sitting inside the triangle — without it, 'opposite' and 'adjacent' don't mean anything. A surveyor's plot, a ship's course change, a garden bed with an odd-angled corner — none of these come with a right angle built in. That's the entire reason the sine rule, cosine rule, and the trig area formula exist: they solve any triangle, not just right-angled ones.
- New at this level: sine rule, cosine rule, and for oblique (non-right-angled) triangles.
- Carried forward: SOH CAH TOA, angles of elevation/depression, Pythagoras' theorem — still essential, just now restricted to right-angled cases.
- Extended into: three-figure bearings, 3D solids (space diagonals, line-to-plane angles), and transformed sine/cosine graphs.
- The examiner's real test throughout: can you tell which formula the given data actually allows you to use?
The shape of the chapter
Command terms this topic loves to test
| Command term | What it demands | AO | Mark-earning move |
|---|---|---|---|
| Calculate | Obtain a numerical answer, with the working/formula visible | AO1/AO2 | Mark needs correct substitution AND correct final value with units — a right answer with no formula shown can still lose the method mark |
| Show that | Prove a given result using the stated method; the answer is already known so every step must be airtight | AO2/AO3 | Zero marks for simply writing down the given answer — exact values (e.g. ) must appear in the substitution |
| State | Give a fact or formula with no working required | AO1 | One mark for the correct statement alone |
| Hence | Use the previous part's result or method — starting a fresh, unconnected method forfeits the mark even if the final number is right | AO2 | Working must visibly build on the earlier answer |
| Advise / Justify | Give a decision (sufficient/insufficient, shorter/longer, yes/no) AND back it with an explicit numeric comparison | AO3 | The decision mark is lost if the comparison number isn't stated, even when the decision itself is correct |
Key point
Overview