How to Memorise the Unit Circle (and Rebuild It in 30 Seconds)
Stop memorising 16 coordinate pairs. Learn the root-n-over-2 pattern, reference angles and quadrant signs, and rebuild the whole unit circle from scratch.
7 min read
Read the guideTrigonify reference
Trigonometry guides
Long-form explanations of the parts of trigonometry that a formula sheet cannot teach you: how to reconstruct the unit circle instead of memorising it, which triangle law a given set of measurements calls for, how to actually prove an identity, and how to find every solution of a trig equation. Each guide is worked through with the same 45 identities in the reference, and every page here is free to read - no account needed.
Law of Sines vs Law of Cosines: Which One to Use (and the Ambiguous SSA Case)
A decision rule for choosing between the law of sines and the law of cosines, four worked triangles, and the SSA ambiguous case explained properly.
9 min read
Read the guideHow to Prove a Trig Identity: A Step-by-Step Method
The five moves that crack almost every trig identity proof, five fully worked examples, and the rule about what you are not allowed to do to both sides.
9 min read
Read the guideSolving Trigonometric Equations: How to Find Every Solution in an Interval
Why trig equations have infinitely many answers, the general-solution formulas for sine, cosine and tangent, and five worked equations including the traps.
10 min read
Read the guideRadians vs Degrees: What a Radian Actually Is and When You Must Use One
What a radian measures, how to convert both ways, and the formulas that are simply wrong in degrees - arc length, sector area and every derivative.
8 min read
Read the guideSOH-CAH-TOA vs the Unit Circle: Two Definitions of the Same Function
How the right-triangle and unit-circle definitions of sine and cosine relate, why the triangle version runs out, and which one to reach for in a problem.
8 min read
Read the guideGraphing Sine and Cosine: Amplitude, Period, Phase Shift and Vertical Shift
Read every transformation straight off y = A sin(B(x − C)) + D, avoid the phase-shift trap, and sketch any sine or cosine curve from five key points.
9 min read
Read the guideInverse Trig Functions: Why arcsin, arccos and arctan Have Restricted Ranges
Why inverse trig functions need restricted ranges, what each range is, and how to evaluate compositions like arcsin(sin 5π/6) and tan(arccos(−1/3)).
8 min read
Read the guidePractise what you read
Every guide points back into the reference, but reading is not recall. The workspace drills the same material in the quiz, and the triangle solver shows a worked solution for any triangle you type in.