Topic Brief: Trig Graphs Period and Domain

Provenance: compiled 2026-09-29. Source is research/veridian/WMA11-verified-facts.md §4.3, §6, §7 and the trig-graphs-period-and-domain.ts lesson-audit-log entry (lines ~1082–1189) — all read in full for this document; no new primary-source PDF was fetched here. Cross-checked against codex-deep-dive-trig-graphs-period-and-domain.md §6 and signal-frequency-and-boundaries.md §1 in this same folder, both already read in full, so this brief does not repeat either document's frequency accounting or general-theory content — it narrows to what those two only summarised: the citation-by-citation exam record for this one spec point. The live lesson trig-graphs-period-and-domain.ts (908 lines) was read in full previously in this course and is not re-summarised here beyond what's needed for scope. Not affiliated with or endorsed by Pearson Edexcel.

#SIGNAL Topic Master Brief — Trig Graphs: Period and Domain (spec 3.3)

#Frequency: seen in 3 of 9 series checked

The facts bank has touched nine WMA11 series in total (Jan 2019, Oct 2020, Oct 2021, Oct 2022, Jan 2023, Jan 2024, Jan 2025, June 2022, June 2023), but at uneven depth — five have a fully-read examiner report (Jan 2019, Oct 2020, Oct 2021, Jan 2023, Jan 2025), two are confirmed-genuine mark schemes never mined question-by-question (Oct 2022, Jan 2024), and two more were each read for one unrelated targeted question only (June 2022 Q5; June 2023 Q1–Q2). A confirmed spec-3.3 question (sine/cosine/tangent graphs, their symmetries and periodicity) exists in 3 of those 9: Jan 2019, Oct 2021, and Jan 2023. Within the five fully-read reports specifically, that's 3 of 5. Oct 2020 and Jan 2025 — both fully read — have no confirmed spec-3.3 finding; the other four series (Oct 2022, Jan 2024, June 2022, June 2023) simply were never checked for this topic, so their absence here means "unread," not "absent."

#The three confirmed appearances

Jan 2023 Q9(a) (1 mark, B1 only, no method line) — "State the period of tan x," attached to a figure showing y = tan x with the line y = πx. Mark scheme, verbatim and in full: "Period is π (radians) but condone 180° or just 180." This is the richest of the three citations — question, mark scheme and examiner report were all independently re-fetched and re-extracted from the primary Pearson PDFs during the course's mark-scheme-bullet audit pass, not taken from commentary alone.

Oct 2021 Q4(a)(i)–(ii) (3 marks total, all B1, no method line) — a figure sketches y = cos 2x° over 0 ≤ x ≤ k, with a minimum point Q and a point R(k, 0) marked; the question asks for the coordinates of Q and the value of k. Real mark scheme: one B1 for either coordinate of Q correct in position, a second B1 for both coordinates fully correct, and a third B1 for k = 225 (the sketch shows one-and-a-quarter periods of a 180°-period curve). This question was originally miscited in the facts bank's own earlier pass as a "describe the transformation" question; re-fetching the actual paper corrected that — it is a coordinate- and period-reading question, not a worded-description one.

Jan 2019 Q5 — sketch y = sin x on axes already drawn for y = cos 2x, with no scale supplied on either graph. This citation rests on examiner-report commentary only; the facts bank has not independently re-extracted a mark scheme for it, so no mark-by-mark breakdown is stated here. The report attributes weaker sketches directly to the missing scale, and separately notes many candidates never marked a scale on their own axis despite being prompted to.

#Mark-tariff pattern: small, method-free, and never the whole question

Every confirmed mark on this topic is a B mark — an independent accuracy mark with no method credit attached — and none of the three anchors is a stand-alone question. Jan 2023 Q9(a) is the low-tariff opening sub-part of a 4-mark question whose remaining three marks (b(i)–(iii)) test a different skill, graph-intersection counting under spec 1.11, not this one. Oct 2021 Q4(a) is the opening 3 marks of a longer multi-part question. On the one series with a full mark-weight reconstruction (Jan 2023), this topic's confirmed contribution to the whole 75-mark paper is exactly 1 mark — the smallest single-topic figure in that reconstruction. The pattern across all three anchors: a handful of B marks, awarded for stating a fact correctly rather than showing a derivation, sitting inside a question that pivots elsewhere for its remaining marks.

#The recurring angle: read it off a given figure, don't derive it from scratch

All three confirmed questions hand the student an already-drawn figure and ask for a specific value or coordinate read from it — a period, a minimum point's coordinates, a companion sketch drawn to match one already on the page — rather than asking for a general derivation or an unfamiliar transformation description in words. None of the three anchors asks "describe the transformation" as free text; that framing appears in this course's own material only as an earlier miscitation of Oct 2021 Q4(a), corrected once the real question paper was checked.

#Confirmed trap set

• Period confused with domain/interval — Jan 2023 Q9(a)'s examiner report: a common wrong answer for the period of tan x was an interval such as −π/2 < x < π/2, which the report attributes to "confusion between period and domain/range."
• Degree form not condoned by default, but is real credit — the same mark scheme explicitly accepts 180° or 180 as equivalent to π; a student who reasons in degrees throughout is not penalised for it on this question.
• Unscaled sketch reduces precision — Jan 2019 Q5's examiner report ties a missing scale on the given cos 2x graph to weaker sin x sketches, and separately flags candidates who never scaled their own axis.
• Partial coordinate credit on Oct 2021 Q4(a) — the mark scheme separates "one coordinate right" from "fully correct," so a half-right point still banks one of the two marks rather than none.

#If this topic appears: what to expect

Expect a small, self-contained sub-part rather than a full question — a handful of B marks for stating a period, a coordinate, or a value read off a figure already on the page, not for showing method. Get the vocabulary distinction right first: a period is a repeat-length, not an interval of validity, and confusing the two is the single most-documented error on this exact spec point. If a degree-form answer is more natural, check whether the scheme condones it (it did on the one series where this was verified) rather than assuming radians are mandatory. And if you're handed a sketch, whether to read from or to draw alongside, put a scale on every axis you use — the one series with sketch-precision commentary ties a missing scale directly to lost marks.