Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

Trigonometry is one of the broadest and most heavily examined sections of Edexcel A-Level Maths (9MA0). It runs across both halves of the pure specification — the Pure 1 content covers radians, trig graphs, basic identities and equation-solving, and the Pure 2 content extends into inverse functions, compound and double angles, harmonic form, reciprocal trig and small-angle approximations. Trigonometry questions appear on every pure paper, often combined with calculus, vectors or coordinate geometry, and they reward candidates who can move fluently between identities and graphical reasoning.

This guide is a topic-by-topic walkthrough of the trigonometry content in the 9MA0 specification. It covers radians and arc-length work, the three primary trig graphs and their transformations, the Pythagorean and quotient identities, inverse trig functions and their domains, compound and double-angle formulae, harmonic form (writing $a\sin\theta + b\cos\theta$ as a single trig function), the small-angle approximations used in Pure 2 calculus questions, the reciprocal functions $\sec\theta$ , $\csc\theta$ and $\cot\theta$ , and the strategies for solving trig equations across an interval. For each topic you will see the core skills, the typical pitfalls, a short worked example or key identity, and a link to the full lesson on the LearningBro course.

The aim is not to replace working through problems. The only way to internalise trigonometry is to do hundreds of questions until the identities feel automatic. The aim is to give you a clear map of what Edexcel can ask, in the order Pure 1 and Pure 2 build it, so your revision is targeted rather than scattered. Use this guide as a checklist, a refresher, and a launchpad into focused practice.

What the Edexcel 9MA0 Specification Covers

The Edexcel A-Level Maths qualification (9MA0) is assessed through three two-hour papers, each worth 100 marks. Papers 1 and 2 cover pure mathematics, and Paper 3 covers statistics and mechanics. Trigonometry sits in Section 5 of the pure specification and is split across Pure 1 and Pure 2 content. There is no choice of questions and no coursework, so every mark must be earned in the exam.

Trigonometry is one of the highest-frequency topic areas on the pure papers. It rarely stands alone — a calculus question will almost always involve differentiating or integrating a trig function, a vector question will use $\cos\theta$ for the angle between two vectors, and a parametric or implicit problem will lean on the Pythagorean identity. The table below shows the sub-topics of Section 5, the part of the specification they sit under, and a realistic estimate of how many marks across a Paper 1 / Paper 2 sitting come from each.

Topic	Spec Section	Typical paper marks weight
Radians, arc length and sector area	5.1	4-6 marks
Trig functions and graphs	5.2	3-5 marks
Trig identities (Pythagorean, quotient)	5.3	4-6 marks
Inverse trig functions	5.4	2-4 marks
Compound-angle formulae	5.5	6-10 marks
Double-angle formulae	5.6	6-10 marks
Harmonic form ( $R\sin(\theta + \alpha)$ )	5.7	6-8 marks
Small-angle approximations	5.8	2-4 marks
Reciprocal trig functions	5.9	3-5 marks
Solving trig equations	5.10	6-10 marks

These weights are estimates based on the spread of typical 9MA0 papers — not guarantees for any single year. What is reliable, however, is that the compound-angle, double-angle and harmonic-form trio is consistently the highest-yield combination on Paper 2, that solving trig equations appears on every paper in some form, and that radians underpin every Pure 2 calculus problem involving trig. Mastering this section is high-leverage revision.

Radians and Arc Length

Radians replace degrees as the standard angle measure from Pure 1 onwards, and Edexcel expects you to use them by default for any calculus or arc-length question. A radian is the angle subtended at the centre of a circle by an arc equal in length to the radius, so a full revolution is $2\pi$ radians, half a revolution is $\pi$ , and a right angle is $\pi/2$ . The conversion is $180^\circ = \pi$ radians, so $1^\circ = \pi/180$ radians.

The two formulae that follow immediately are arc length $s = r\theta$ and sector area $A = \frac{1}{2}r^2\theta$ , where $\theta$ is in radians. Both fail if you accidentally feed in degrees, so always convert first. The chord length subtended by an angle $\theta$ at the centre of a circle of radius $r$ is given by the cosine rule and equals $2r\sin(\theta/2)$ — a result worth knowing because it appears in segment-area questions.

A common pitfall is leaving your calculator in degree mode for a radian question (or vice versa). Get into the habit of checking the mode indicator before every trig question. Another pitfall is mixing up arc length and sector area — the arc-length formula has no $\frac{1}{2}$ and is linear in $\theta$ , while the sector-area formula has the $\frac{1}{2}$ and the $r^2$ .

A short worked example. A sector of a circle of radius $6$ cm subtends an angle of $\pi/3$ at the centre. The arc length is $s = 6 \times \pi/3 = 2\pi$ cm, and the sector area is $A = \frac{1}{2} \times 6^2 \times \pi/3 = 6\pi$ cm $^2$ . Notice both answers are left in exact form involving $\pi$ — Edexcel expects exact answers unless the question asks for a decimal.

For full coverage with practice questions and worked solutions, see the Radians lesson.

Trigonometric Functions and Graphs

You should know the graphs of $y = \sin\theta$ , $y = \cos\theta$ and $y = \tan\theta$ from memory: their period, amplitude, intercepts, asymptotes (for tangent), and key features. Sine and cosine both have period $2\pi$ and oscillate between $-1$ and $1$ . Tangent has period $\pi$ and vertical asymptotes at $\theta = \pi/2 + n\pi$ for integer $n$ . The cosine graph is simply the sine graph translated $\pi/2$ to the left, encoded by the identity $\cos\theta = \sin(\theta + \pi/2)$ .

Once the basic graphs are secure, you should be able to apply graph transformations from the Algebra and Functions section to trig functions confidently. $y = 2\sin\theta$ is a vertical stretch, doubling the amplitude. $y = \sin(2\theta)$ is a horizontal stretch by factor $1/2$ , halving the period. $y = \sin(\theta - \pi/4)$ is a translation $\pi/4$ to the right. Combined transformations like $y = 3\cos(2\theta + \pi/3)$ require the same care over order as in the algebra section — handle the inside-bracket transformations first.

A common pitfall is misreading the period of $\sin(k\theta)$ as $2\pi/k$ (correct) but then sketching a graph with $k$ extra peaks per $2\pi$ rather than the correct number. Another is forgetting the asymptotes on a tangent graph or drawing them in the wrong place after a translation.

A useful sketch reflex: for any transformed sine or cosine graph, identify the new amplitude, the new period, and any horizontal or vertical translation. Plot the new midline first, then a single full period at the new amplitude, then extend.

For sketching practice and transformation drills on all three primary graphs, see the Trig Functions and Graphs lesson.

Trigonometric Identities

The two foundational identities that every A-Level question assumes are the Pythagorean identity and the quotient identity:

$\cos^2\theta + \sin^2\theta = 1, \qquad \tan\theta = \frac{\sin\theta}{\cos\theta}.$

From these two you can derive everything else in the Pure 1 identities toolkit. Dividing the Pythagorean identity through by $\cos^2\theta$ gives $1 + \tan^2\theta = \sec^2\theta$ . Dividing through by $\sin^2\theta$ gives $\cot^2\theta + 1 = \csc^2\theta$ . These two derived identities sit at the heart of integration questions involving $\sec^2\theta$ or $\csc^2\theta$ and should be as automatic as the original.

Edexcel uses these identities in two different question types. The first is a prove that question: rearrange one side until it equals the other, using only standard identities. The second is an equation-solving question where the equation contains a mix of $\sin\theta$ , $\cos\theta$ and $\tan\theta$ , and you use the quotient identity or Pythagorean identity to reduce to a single trig function before solving.

A short worked example of a proof. Show that $\frac{1 - \cos^2\theta}{\sin\theta\cos\theta} = \tan\theta$ . The numerator is $\sin^2\theta$ by the Pythagorean identity, so the left-hand side becomes $\frac{\sin^2\theta}{\sin\theta\cos\theta} = \frac{\sin\theta}{\cos\theta} = \tan\theta$ . Notice the move was a one-step substitution followed by a clean cancellation.

A common pitfall is reaching for compound or double-angle identities when a Pure 1 Pythagorean identity would do. Always check the simpler tools first. Another is mis-stating the identity as $\sin^2\theta - \cos^2\theta = 1$ — the order matters for memory but the sum is what is constant.

For worked proofs and identity-driven equations, see the Trig Identities lesson.

Inverse Trigonometric Functions

The inverse trigonometric functions $\arcsin$ , $\arccos$ and $\arctan$ undo the corresponding trig functions, returning an angle from a given ratio. Because sine, cosine and tangent are not one-to-one over their full domain, the inverses are defined on restricted ranges so that they produce a unique output.

Function	Domain	Range
$\arcsin x$	$-1 \leq x \leq 1$	$-\pi/2 \leq y \leq \pi/2$
$\arccos x$	$-1 \leq x \leq 1$	$0 \leq y \leq \pi$
$\arctan x$	all real $x$	$-\pi/2 < y < \pi/2$

You should be able to sketch each inverse graph from memory: $\arcsin$ rises from $(-1, -\pi/2)$ to $(1, \pi/2)$ , $\arccos$ falls from $(-1, \pi)$ to $(1, 0)$ , and $\arctan$ rises from a horizontal asymptote at $y = -\pi/2$ through the origin to a horizontal asymptote at $y = \pi/2$ . Each inverse graph is the reflection of the corresponding original (restricted) graph in the line $y = x$ .

A common pitfall is forgetting that $\arcsin(\sin\theta)$ is not always equal to $\theta$ — it returns the value in $[-\pi/2, \pi/2]$ that has the same sine, which may be $\pi - \theta$ or some other angle if $\theta$ lies outside the principal range. Another is treating $\arcsin$ , $\arccos$ and $\arctan$ as their reciprocals (they are not — those are $\csc$ , $\sec$ and $\cot$ ).

For sketching practice and domain-range drills on all three inverses, see the Inverse Trig lesson.

Compound-Angle Formulae

The compound-angle formulae express $\sin(A \pm B)$ , $\cos(A \pm B)$ and $\tan(A \pm B)$ in terms of the trig values of $A$ and $B$ separately. They are the gateway to almost every Pure 2 trig topic — double angles, harmonic form, and many integration techniques all rely on them. Memorise them in the standard form:

$\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B,$ $\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B,$ $\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}.$

The sign rule is the trickiest part. For sine, the sign on the right matches the sign on the left. For cosine, the sign on the right is the opposite of the sign on the left — hence the $\mp$ symbol. For tangent, the numerator sign matches and the denominator sign is opposite. Working through a few derivations from $\cos(A + B)$ via the sine and cosine product expansions is the best way to lock the signs in.

Edexcel uses compound-angle formulae for three main question types. The first is computing an exact value like $\sin(75^\circ) = \sin(45^\circ + 30^\circ)$ . The second is proving identities — for example, showing that $\sin(A + B) - \sin(A - B) = 2\cos A \sin B$ . The third is feeding into harmonic form, where compound angles are reversed to combine $a\sin\theta + b\cos\theta$ into a single $R\sin(\theta + \alpha)$ .

A common pitfall is mis-remembering the cosine sign rule and writing $\cos(A + B) = \cos A \cos B + \sin A \sin B$ — that is the formula for $\cos(A - B)$ , not $\cos(A + B)$ . Another is applying the formulae in degrees but having the calculator in radian mode, or vice versa.

For full derivations and worked examples in all three question types, see the Compound Angles lesson.

Double-Angle Formulae

The double-angle formulae are the special case of the compound-angle formulae when $A = B$ . They are worth memorising independently because they appear so often:

$\sin 2\theta = 2\sin\theta\cos\theta,$ $\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta,$ $\tan 2\theta = \frac{2\tan\theta}{1 - \tan^2\theta}.$

The cosine double-angle formula has three equivalent forms. Which form you use depends on what is in the rest of the question. If the equation already contains $\cos^2\theta$ , use $\cos 2\theta = 2\cos^2\theta - 1$ and rearrange to $\cos^2\theta = (1 + \cos 2\theta)/2$ . If it contains $\sin^2\theta$ , use $\cos 2\theta = 1 - 2\sin^2\theta$ , giving $\sin^2\theta = (1 - \cos 2\theta)/2$ . These two rearrangements are essential for integrating $\sin^2\theta$ and $\cos^2\theta$ in Pure 2 calculus.

A short worked example. Solve $\cos 2\theta + \sin\theta = 0$ for $0 \leq \theta < 2\pi$ . Use $\cos 2\theta = 1 - 2\sin^2\theta$ to rewrite as $1 - 2\sin^2\theta + \sin\theta = 0$ , or $2\sin^2\theta - \sin\theta - 1 = 0$ . Factorise as $(2\sin\theta + 1)(\sin\theta - 1) = 0$ , giving $\sin\theta = -1/2$ or $\sin\theta = 1$ . The solutions in the interval are $\theta = \pi/2, 7\pi/6, 11\pi/6$ .

Common pitfalls include picking the wrong form of $\cos 2\theta$ for the question — usually the right choice is the one that turns the equation into a quadratic in a single trig function. Another is forgetting that $\sin 2\theta$ has period $\pi$ , not $2\pi$ , so an interval of $0 \leq \theta < 2\pi$ for the original variable corresponds to $0 \leq 2\theta < 4\pi$ for the double angle, doubling the number of solutions.

For drilling all three forms of $\cos 2\theta$ and the standard rearrangements, see the Double Angles lesson.

Harmonic Form

Harmonic form is the technique of writing $a\sin\theta + b\cos\theta$ as a single sinusoid $R\sin(\theta + \alpha)$ or $R\cos(\theta - \alpha)$ . It is one of the highest-yield topics in Pure 2 because it converts an awkward two-term expression into a single trig function whose maximum, minimum and zeros can be read off immediately.

The standard workflow is as follows. Suppose you want $a\sin\theta + b\cos\theta = R\sin(\theta + \alpha)$ . Expanding the right-hand side using the compound-angle formula gives $R\sin\theta\cos\alpha + R\cos\theta\sin\alpha$ . Equating coefficients of $\sin\theta$ and $\cos\theta$ gives $R\cos\alpha = a$ and $R\sin\alpha = b$ . Squaring and adding yields $R^2 = a^2 + b^2$ , so $R = \sqrt{a^2 + b^2}$ . Dividing yields $\tan\alpha = b/a$ , so $\alpha = \arctan(b/a)$ — taking care to put $\alpha$ in the correct quadrant based on the signs of $a$ and $b$ .

You should know all four harmonic-form templates, because Edexcel can ask for any of them:

Template	Conditions on coefficients
$a\sin\theta + b\cos\theta = R\sin(\theta + \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\sin\theta - b\cos\theta = R\sin(\theta - \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\cos\theta + b\sin\theta = R\cos(\theta - \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\cos\theta - b\sin\theta = R\cos(\theta + \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$

Once you have rewritten the expression in harmonic form, the maximum is $R$ (when the inner trig function equals $1$ ) and the minimum is $-R$ (when it equals $-1$ ). For an equation like $a\sin\theta + b\cos\theta = c$ , rewrite as $R\sin(\theta + \alpha) = c$ , then $\sin(\theta + \alpha) = c/R$ , then solve as a standard trig equation.

A common pitfall is mis-identifying $\alpha$ when $a$ or $b$ is negative — make sure your $\alpha$ lies in the correct quadrant given the signs. Another is matching the wrong template to the question; always read which trig function is leading and whether the coefficients are added or subtracted before assigning $R$ and $\alpha$ .

For full template comparison and worked maximum/minimum and equation problems, see the Harmonic Form lesson.

Small-Angle Approximations

For small angles measured in radians, the following approximations hold:

$\sin\theta \approx \theta, \qquad \cos\theta \approx 1 - \frac{\theta^2}{2}, \qquad \tan\theta \approx \theta.$

These come from the Maclaurin series of the trig functions and are accurate to good precision when $\theta$ is small (typically $|\theta| < 0.1$ or so). Edexcel uses small-angle approximations in two main settings: estimating values of trig functions at small angles, and proving certain limits or simplifying expressions in calculus problems involving trig functions.

The approximations only work in radians. In degrees they are off by a factor of $\pi/180$ and the question becomes nonsense — this is why every small-angle question explicitly stipulates radians. They are also one-sided in spirit: the smaller $\theta$ is, the better the approximation.

A short worked example. Estimate $\sin(0.05)$ . Using the small-angle approximation, $\sin(0.05) \approx 0.05$ . The true value is $0.04998$ , so the approximation is accurate to four decimal places. For $\cos(0.05)$ , $\cos(0.05) \approx 1 - 0.05^2/2 = 1 - 0.00125 = 0.99875$ , agreeing with the true value to five decimal places.

A common pitfall is using small-angle approximations for angles that are not small — they break down quickly above $\theta \approx 0.3$ . Another is forgetting that the cosine approximation requires the $-\theta^2/2$ term; using $\cos\theta \approx 1$ alone is too crude for any A-Level question that asks for a numerical estimate.

For derivations and worked estimation problems, see the Small-Angle Approximations lesson.

Reciprocal Trig Functions

The reciprocal trig functions are defined as the reciprocals of the primary three:

$\sec\theta = \frac{1}{\cos\theta}, \qquad \csc\theta = \frac{1}{\sin\theta}, \qquad \cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}.$

Each has its own graph with vertical asymptotes wherever the original function equals zero. $\sec\theta$ has asymptotes at $\theta = \pi/2 + n\pi$ (where $\cos\theta = 0$ ). $\csc\theta$ has asymptotes at $\theta = n\pi$ (where $\sin\theta = 0$ ). $\cot\theta$ has asymptotes at $\theta = n\pi$ (where $\tan\theta$ is zero) and zeros at $\theta = \pi/2 + n\pi$ . You should be able to sketch each from memory.

The two derived Pythagorean identities involving the reciprocal functions are:

$1 + \tan^2\theta = \sec^2\theta, \qquad 1 + \cot^2\theta = \csc^2\theta.$

These appear constantly in trig equations involving $\sec$ or $\csc$ , and in integration questions where the integrand simplifies cleanly with one of them. The standard rearrangement $\sec^2\theta - 1 = \tan^2\theta$ is particularly useful when an equation contains both $\sec\theta$ and $\tan\theta$ .

A common pitfall is confusing the reciprocal functions with the inverse functions. $\sec\theta$ is $1/\cos\theta$ and is a function of an angle; $\arcsec\theta$ (rarely used at A-Level) is the inverse, returning an angle. Another is sketching the reciprocal graphs without first sketching the primary graph in faint outline — the asymptotes and turning points of the reciprocal sit exactly where the primary has zeros and extrema, so the primary is a useful scaffold.

For sketching practice and identity drills, see the Reciprocal Trig lesson.

Solving Trigonometric Equations

Solving a trig equation for all solutions in a given interval is the single most common type of trig question on the 9MA0 papers. The general workflow is:

Reduce to a single trig function using identities (Pythagorean, quotient, double-angle, harmonic). This is the step where most marks are won or lost.
Find the principal value using the inverse trig function on your calculator.
Find all solutions in the given interval by adding the period (and using the symmetry of the trig graph to find any other solutions in the same period).
Check the interval endpoints — make sure every solution you write down lies inside the stated interval.

For a sine equation $\sin\theta = k$ in $[0, 2\pi)$ , the principal value is $\theta_1 = \arcsin k$ . The second solution in the interval is $\theta_2 = \pi - \theta_1$ , by the symmetry of the sine graph about $\theta = \pi/2$ . For a cosine equation $\cos\theta = k$ , the principal value is $\theta_1 = \arccos k$ , and the second solution is $\theta_2 = 2\pi - \theta_1$ , by the symmetry of the cosine graph about $\theta = \pi$ . For a tangent equation $\tan\theta = k$ , the principal value is $\theta_1 = \arctan k$ and further solutions are at $\theta_1 + n\pi$ for integer $n$ .

When the equation involves $k\theta$ rather than $\theta$ — for instance $\sin(2\theta) = 1/2$ for $0 \leq \theta < 2\pi$ — the standard trick is to first widen the interval to match the new variable. Let $\phi = 2\theta$ , so $0 \leq \phi < 4\pi$ . Solve $\sin\phi = 1/2$ across $[0, 4\pi)$ , finding all four solutions, then divide each by $2$ to recover $\theta$ .

A short worked example. Solve $2\cos^2\theta - \cos\theta - 1 = 0$ for $0 \leq \theta < 2\pi$ . Factorise as $(2\cos\theta + 1)(\cos\theta - 1) = 0$ , giving $\cos\theta = -1/2$ or $\cos\theta = 1$ . From $\cos\theta = -1/2$ : $\theta = 2\pi/3, 4\pi/3$ . From $\cos\theta = 1$ : $\theta = 0$ . The full solution set is $\theta = 0, 2\pi/3, 4\pi/3$ .

A common pitfall is finding the principal value and stopping there, missing the second (or third, or fourth) solution in the interval. Another is forgetting to widen the interval when the trig function has a coefficient inside the bracket. A third is rounding too early — keep solutions in exact form whenever the cosine or sine takes a familiar exact value (such as $1/2$ , $\sqrt{2}/2$ or $\sqrt{3}/2$ ).

For full coverage of single-function and identity-reduction trig equations, see the Trig Equations lesson.

Common Mark-Loss Patterns Across Trigonometry

Across the whole trigonometry section, a small set of habits accounts for a disproportionate share of lost marks. None of these are about content you do not know. They are all about content you do know, applied carelessly.

Calculator in the wrong mode. Degrees instead of radians, or vice versa. Always check the mode indicator before any trig calculation.
Missing solutions in the interval. A common pitfall is finding only the principal value and stopping there. Sketch the trig graph in the interval to see all solutions visually before writing them down.
Wrong sign in compound or double-angle formulae. $\cos(A + B) = \cos A \cos B - \sin A \sin B$ has a minus; $\cos(A - B)$ has a plus. The signs are easy to flip under exam pressure.
Forgetting to widen the interval when the equation contains $\sin(k\theta)$ or $\cos(k\theta)$ for $k \neq 1$ . The number of solutions multiplies by $k$ .
Picking the wrong form of $\cos 2\theta$ . The right choice usually reduces the equation to a quadratic in a single trig function. Look at what the rest of the equation contains before substituting.
Mis-placing $\alpha$ in harmonic form. Always check the quadrant of $\alpha$ against the signs of $a$ and $b$ .
Using small-angle approximations in degrees. The approximations hold only in radians.
Confusing reciprocal and inverse functions. $\sec\theta$ is $1/\cos\theta$ , not $\arccos\theta$ .
Cancelling $\cos\theta$ across an equation. Dividing through by $\cos\theta$ loses the solutions where $\cos\theta = 0$ . Always factorise instead and use the zero-product rule.
Not showing enough working. Edexcel mark schemes award method marks generously when the working is clear. A correct final answer with no working can score fewer marks than an incorrect final answer with clean method.

Many candidates lose marks here every series. A revision plan that explicitly drills these habits — not just the content — will move your grade more than another pass through the textbook.

Exam Strategy and High-Yield Topics for May 2026

Trigonometry rewards strategic revision because the content is uneven in weight. A small number of topics carry a disproportionate share of the marks, and three in particular form the highest-yield combination on Paper 2: compound-angle formulae, double-angle formulae, and harmonic form. These three together typically account for 18-25 marks across a Paper 2 sitting, and they reinforce each other — fluency with compound angles makes double angles immediate, and harmonic form is essentially a structured application of the compound-angle expansion in reverse. Drilling these three together for a week is one of the highest-leverage things you can do in the final fortnight.

The next tier of high-yield topics is solving trig equations (which appears on every paper, often combined with one of the above three) and radians (which underpins every Pure 2 calculus question involving trig). Both are reliable mark-banks if you have the workflow down: reduce-to-single-function for equations, and convert-and-apply for radian arc/sector work.

The third tier is identities, reciprocal functions, and graph-and-transformation work. These are the steady earners — usually 4-6 marks each, accessible once the headline topics are secure. Inverse trig and small-angle approximations are the lowest-weight topics in the section, but small-angle approximations are worth knowing well because they unlock certain calculus questions that would otherwise be intractable.

For the final two weeks before the exam, a sensible split is: three days on compound and double angles, three days on harmonic form (including maximum/minimum and equation applications), three days on solving trig equations (including the widen-the-interval trick), two days on radians and identities, and the remainder on mixed-topic past papers. By the last day, you should be able to look at any trig question and recognise the topic in seconds, even if the algebra takes longer.

The single highest-value habit through this plan is sketching the trig graph for any equation you solve. A 30-second sketch makes "missed solutions" almost impossible and turns an algebra problem into a visual one.

Where to Go from Here

LearningBro's Edexcel A-Level Maths: Trigonometry course is built around the structure of this guide. Each of the ten lessons covers one section of the 9MA0 trigonometry specification, in the order Pure 1 and Pure 2 build the topics, with worked examples, practice questions and full mark-scheme-style solutions. Lessons end with a short review and quick-recall questions designed for spaced revisits.

The course is designed to be used in two ways. As a first pass, you can work through the lessons in order, building each topic on the last — radians underpins arc length, identities feed compound angles, compound angles feed double angles and harmonic form, and trig equations brings everything together. As a revision tool, you can drop into any lesson and work the practice independently — for example, drilling harmonic form for a week before mocks. The AI tutor is available throughout to give targeted hints when you get stuck, without giving away full solutions, and to mark your written working with structured feedback.

If you want one place to revise this section of the spec well, with realistic practice and clean explanations of every topic, the full course is the right next step. Start with the Edexcel A-Level Maths: Trigonometry course.

Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

What the Edexcel 9MA0 Specification Covers

Topic	Spec Section	Typical paper marks weight
Radians, arc length and sector area	5.1	4-6 marks
Trig functions and graphs	5.2	3-5 marks
Trig identities (Pythagorean, quotient)	5.3	4-6 marks
Inverse trig functions	5.4	2-4 marks
Compound-angle formulae	5.5	6-10 marks
Double-angle formulae	5.6	6-10 marks
Harmonic form ( $R\sin(\theta + \alpha)$ )	5.7	6-8 marks
Small-angle approximations	5.8	2-4 marks
Reciprocal trig functions	5.9	3-5 marks
Solving trig equations	5.10	6-10 marks

Radians and Arc Length

For full coverage with practice questions and worked solutions, see the Radians lesson.

Trigonometric Functions and Graphs

For sketching practice and transformation drills on all three primary graphs, see the Trig Functions and Graphs lesson.

Trigonometric Identities

The two foundational identities that every A-Level question assumes are the Pythagorean identity and the quotient identity:

$\cos^2\theta + \sin^2\theta = 1, \qquad \tan\theta = \frac{\sin\theta}{\cos\theta}.$

For worked proofs and identity-driven equations, see the Trig Identities lesson.

Inverse Trigonometric Functions

Function	Domain	Range
$\arcsin x$	$-1 \leq x \leq 1$	$-\pi/2 \leq y \leq \pi/2$
$\arccos x$	$-1 \leq x \leq 1$	$0 \leq y \leq \pi$
$\arctan x$	all real $x$	$-\pi/2 < y < \pi/2$

For sketching practice and domain-range drills on all three inverses, see the Inverse Trig lesson.

Compound-Angle Formulae

$\sin(A \pm B) = \sin A \cos B \pm \cos A \sin B,$ $\cos(A \pm B) = \cos A \cos B \mp \sin A \sin B,$ $\tan(A \pm B) = \frac{\tan A \pm \tan B}{1 \mp \tan A \tan B}.$

For full derivations and worked examples in all three question types, see the Compound Angles lesson.

Double-Angle Formulae

The double-angle formulae are the special case of the compound-angle formulae when $A = B$ . They are worth memorising independently because they appear so often:

$\sin 2\theta = 2\sin\theta\cos\theta,$ $\cos 2\theta = \cos^2\theta - \sin^2\theta = 2\cos^2\theta - 1 = 1 - 2\sin^2\theta,$ $\tan 2\theta = \frac{2\tan\theta}{1 - \tan^2\theta}.$

For drilling all three forms of $\cos 2\theta$ and the standard rearrangements, see the Double Angles lesson.

Harmonic Form

You should know all four harmonic-form templates, because Edexcel can ask for any of them:

Template	Conditions on coefficients
$a\sin\theta + b\cos\theta = R\sin(\theta + \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\sin\theta - b\cos\theta = R\sin(\theta - \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\cos\theta + b\sin\theta = R\cos(\theta - \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$
$a\cos\theta - b\sin\theta = R\cos(\theta + \alpha)$	$R\cos\alpha = a$ , $R\sin\alpha = b$

For full template comparison and worked maximum/minimum and equation problems, see the Harmonic Form lesson.

Small-Angle Approximations

For small angles measured in radians, the following approximations hold:

$\sin\theta \approx \theta, \qquad \cos\theta \approx 1 - \frac{\theta^2}{2}, \qquad \tan\theta \approx \theta.$

For derivations and worked estimation problems, see the Small-Angle Approximations lesson.

Reciprocal Trig Functions

The reciprocal trig functions are defined as the reciprocals of the primary three:

$\sec\theta = \frac{1}{\cos\theta}, \qquad \csc\theta = \frac{1}{\sin\theta}, \qquad \cot\theta = \frac{1}{\tan\theta} = \frac{\cos\theta}{\sin\theta}.$

The two derived Pythagorean identities involving the reciprocal functions are:

$1 + \tan^2\theta = \sec^2\theta, \qquad 1 + \cot^2\theta = \csc^2\theta.$

For sketching practice and identity drills, see the Reciprocal Trig lesson.

Solving Trigonometric Equations

Solving a trig equation for all solutions in a given interval is the single most common type of trig question on the 9MA0 papers. The general workflow is:

Reduce to a single trig function using identities (Pythagorean, quotient, double-angle, harmonic). This is the step where most marks are won or lost.
Find the principal value using the inverse trig function on your calculator.
Find all solutions in the given interval by adding the period (and using the symmetry of the trig graph to find any other solutions in the same period).
Check the interval endpoints — make sure every solution you write down lies inside the stated interval.

For full coverage of single-function and identity-reduction trig equations, see the Trig Equations lesson.

Common Mark-Loss Patterns Across Trigonometry

Calculator in the wrong mode. Degrees instead of radians, or vice versa. Always check the mode indicator before any trig calculation.
Missing solutions in the interval. A common pitfall is finding only the principal value and stopping there. Sketch the trig graph in the interval to see all solutions visually before writing them down.
Wrong sign in compound or double-angle formulae. $\cos(A + B) = \cos A \cos B - \sin A \sin B$ has a minus; $\cos(A - B)$ has a plus. The signs are easy to flip under exam pressure.
Forgetting to widen the interval when the equation contains $\sin(k\theta)$ or $\cos(k\theta)$ for $k \neq 1$ . The number of solutions multiplies by $k$ .
Picking the wrong form of $\cos 2\theta$ . The right choice usually reduces the equation to a quadratic in a single trig function. Look at what the rest of the equation contains before substituting.
Mis-placing $\alpha$ in harmonic form. Always check the quadrant of $\alpha$ against the signs of $a$ and $b$ .
Using small-angle approximations in degrees. The approximations hold only in radians.
Confusing reciprocal and inverse functions. $\sec\theta$ is $1/\cos\theta$ , not $\arccos\theta$ .
Cancelling $\cos\theta$ across an equation. Dividing through by $\cos\theta$ loses the solutions where $\cos\theta = 0$ . Always factorise instead and use the zero-product rule.
Not showing enough working. Edexcel mark schemes award method marks generously when the working is clear. A correct final answer with no working can score fewer marks than an incorrect final answer with clean method.

Many candidates lose marks here every series. A revision plan that explicitly drills these habits — not just the content — will move your grade more than another pass through the textbook.

Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

What the Edexcel 9MA0 Specification Covers

Radians and Arc Length

Trigonometric Functions and Graphs

Trigonometric Identities

Inverse Trigonometric Functions

Compound-Angle Formulae

Double-Angle Formulae

Harmonic Form

Small-Angle Approximations

Reciprocal Trig Functions

Solving Trigonometric Equations

Common Mark-Loss Patterns Across Trigonometry

Exam Strategy and High-Yield Topics for May 2026

Where to Go from Here

Related Reading

Stay in the loop

Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

Edexcel A-Level Maths: Trigonometry — Complete Revision Guide (9MA0)

What the Edexcel 9MA0 Specification Covers

Radians and Arc Length

Trigonometric Functions and Graphs

Trigonometric Identities

Inverse Trigonometric Functions

Compound-Angle Formulae

Double-Angle Formulae

Harmonic Form

Small-Angle Approximations

Reciprocal Trig Functions

Solving Trigonometric Equations

Common Mark-Loss Patterns Across Trigonometry

Exam Strategy and High-Yield Topics for May 2026

Where to Go from Here

Related Reading

Stay in the loop