17 topics
Trigonometry help, from the unit circle to identities
Trigonometry is where a lot of otherwise-fine math students fall off, and the reason is usually one unfixed gap: the unit circle was memorised as a table of thirty numbers rather than understood as one triangle reflected into four quadrants. Everything downstream — identities, equations, graphs — inherits that gap.
Where students get stuck
I can't memorise the unit circle
You are not supposed to. There are two triangles, 30-60-90 and 45-45-90, and every value on the circle is one of their side ratios with a sign attached. Learn the two triangles, learn which functions are positive in which quadrant, and the thirty values reconstruct themselves in about four seconds each. Memorising the table is strictly harder than not memorising it.
Proving identities — I don't know which side to work on
Work on the messier side and only on that side, until it looks like the other. Never work both sides toward the middle: that assumes the identity is true, which is the thing you are proving. When stuck, convert everything to sine and cosine — it is not elegant but it terminates, and a proof that finishes beats a clever one that stalls.
I only get one answer when the question wants all of them
The inverse functions on your calculator return one value from a restricted range, but sin θ = 0.5 has infinitely many solutions. Find the reference angle, place it in every quadrant where the sign matches, then add the period times n. Losing the second quadrant solution is the single most common error on a trig equations test.
Sine law, cosine law, or neither?
Count what you have. Two angles and any side, or two sides and an angle opposite one of them, means sine law. Three sides, or two sides with the angle between them, means cosine law. The SSA case is the ambiguous one and it can genuinely have two valid triangles — if a question looks like it has two answers there, it probably does.
What's covered
Trigonometry topics you can work through with a tutor, generate practice on, or turn into flashcards and a study plan.
Foundations
- Right triangle ratios and SOH CAH TOA
- Degrees, radians, and conversion
- The unit circle and exact values
- Reference angles and quadrant signs
- Reciprocal and inverse trig functions
Triangles
- The sine law and the ambiguous case
- The cosine law
- Area of a triangle without the height
- Bearings, angles of elevation and depression
Identities and equations
- Pythagorean, quotient, and reciprocal identities
- Sum, difference, and double angle formulas
- Proving identities
- Solving trig equations over an interval and in general form
Graphs
- Amplitude, period, phase shift, and vertical shift
- Graphing sine, cosine, and tangent
- Writing an equation from a graph
- Modelling periodic phenomena
Trigonometry questions
Does it work in radians or degrees?
Both, and it will follow whichever your course uses — just say so, or share the assignment and it will read the convention off the question. Mixed-mode errors are common enough that it will flag it if your working switches partway.
Can it help me actually see what a phase shift does?
Yes. The whiteboard sketches the transformed graph against the base graph so the shift, stretch and reflection are visible as changes rather than as parameters in an equation. The Visual Explainer can also turn a transformations unit into a short narrated walkthrough you can rewatch.
I need practice with identities specifically. Can I get more of those?
Yes — generate a practice set narrowed to proving identities and it will produce fresh problems with full worked proofs, not just a final line.
Stuck on trigonometry right now?
Talk it through out loud, share your screen, and watch it worked out step by step on a whiteboard.
Start free — no card