Trigonometry readiness starts with ratios, not triangles

Sixty-four concepts, and most of them are not triangles

The diagnostic is scoped to angles of elevation and depression, which closes the right-triangle trigonometry section and is the first place the subject is pointed at a real problem rather than a labelled diagram. Its prerequisite closure is 64 concepts across 12 sections in four chapters, and six to ten adaptive questions are usually enough to place you inside it.

The trigonometry itself is six of those 64: identifying the opposite, adjacent and hypotenuse sides relative to a chosen acute angle, the sine, cosine and tangent of an acute angle, the SOHCAHTOA mnemonic, and solving for an unknown side. Most people arriving at this page already hold several of them, which is exactly why a check scoped only to them would tell you nothing.

The geometry is eight more: point, line and plane, the ray, the line segment, the definition of an angle, the right angle, the acute angle, the definition of a triangle and the right triangle. Thin, and rarely the problem. The remaining 50 concepts are arithmetic and algebra, and that is the honest headline of this page.

Why a whole equations section sits inside a trigonometry check

Because sine equals opposite over hypotenuse is a ratio equation, and nearly every question a first course asks with it is a rearrangement. Given the angle and the hypotenuse, find the opposite side: multiply through. Given two sides, find the angle: apply an inverse. Given an elevation angle and a ground distance, find a height: build the equation first, then solve it. The trigonometry supplies one line of that; the equation skills supply the other three.

So the closure pulls in the whole one-variable linear equations section rather than a sample of it: equation as a balance, one-step equations by addition or subtraction, one-step by multiplication or division, two-step equations and multi-step equations. Multi-step is in there specifically because elevation and depression problems generate it, with an unknown sitting inside a fraction, a constant to move, and then a division. A student who can only run one-step equations will pass the SOHCAHTOA questions and stall on the word problems, and from the outside that looks like a trigonometry gap. It is not one.

The other frequent profile is a ratio gap rather than an equation gap. The definition of a ratio and fraction as part of a whole both sit in the closure because sine is not a number attached to an angle. It is a comparison between two lengths that holds fixed when the triangle is scaled. Someone who has never had that said out loud can compute sines correctly for a term and still be quietly confused about why the answer does not depend on how big the triangle is.

What each result should change about your next week

Gaps in one-variable linear equations. Close these before touching trigonometry, and close them with trigonometry-shaped equations rather than generic ones: an unknown in a numerator, an unknown in a denominator, then a two-step version of each. It is the highest-leverage item on any result this check produces.

Gaps in ratios or fractions. Short to close and worth doing slowly, because every later idea in the subject is a ratio in disguise. That includes the unit circle, which is these same three ratios with the hypotenuse pinned to one.

Gaps in the integers block or in order of operations. Common, and usually dismissed. Elevation and depression problems mix upward and downward displacements, and a sign error there produces a plausible wrong height rather than an obvious absurdity, so it survives your own checking.

Gaps only in the six trigonometric concepts themselves. This is the best result available, because it means the foundation is sound and the subject is genuinely ahead of you rather than behind you. Start at the top of the right-triangle section and expect to move quickly.

The limits of what this can tell you

It stops at right-triangle trigonometry. The unit circle, radians, trigonometric graphs, identities, trigonometric equations, the sine and cosine rules and polar coordinates all sit downstream of the target, so none of them is probed. Those are six further sections of the chapter, and a clean result here is a statement about the first one.

It also does not check whether you can draw the diagram. A large share of elevation and depression errors are made before any trigonometry happens, in deciding which angle is the angle of depression and which side is opposite it. A short adaptive check can sample that skill but not really assess it, so practise it on paper whatever your result says.

And it says nothing about your calculator. Degree mode against radian mode is the single most common source of a wrong trigonometric answer in a first course, and it is a settings problem rather than a knowledge problem, so no prerequisite check will ever catch it for you.