Trigonometry

Edexcel Pure 5

A-level Maths (9MA0) · exam-style practice, examiner-report intelligence and the tools that drill it.

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Edexcel 9MA0 revision notes Edexcel 9MA0 past papers

The topic on one screen

Radians for anything with calculus or sectors: arc length $= r\theta$ , sector area $= \tfrac{1}{2}r^2\theta$ .
The two identities that solve most equations: $\sin^2 x + \cos^2 x = 1$ and $\tan x = \dfrac{\sin x}{\cos x}$ .
Harmonic form: $a\cos\theta + b\sin\theta = R\cos(\theta \pm \alpha)$ with $R = \sqrt{a^2 + b^2}$ and $\tan\alpha = \dfrac{b}{a}$ — then max/min and solving become one-liners.
Solving in a range: get ALL solutions — draw the CAST diagram or the graph, don't stop at the calculator value.
Trig modelling (wheels, tides, stages): amplitude = half the max-min gap, the constant = the midline, period $= \dfrac{360}{k}$ (degrees) or $\dfrac{2\pi}{k}$ (radians).
Small-angle approximations (radians only): $\sin\theta \approx \theta$ , $\tan\theta \approx \theta$ , $\cos\theta \approx 1 - \tfrac{\theta^2}{2}$ .

Where students actually lose marks

In $R\cos(\theta + \alpha)$ questions, $R$ must be exact and positive — and the mark scheme wants $\alpha$ to the stated accuracy. A rounded $R$ poisons every later part.

June 2024 Paper 1 mark scheme (Q12)

Sector questions mix degrees and radians as a trap: the formulas $r\theta$ and $\tfrac{1}{2}r^2\theta$ are RADIAN formulas — using 2.3 rad in a degree formula (or vice versa) voids the method mark.

June 2023 Paper 1 question paper (Q08, angle given in radians)

In trig-equation solving the scheme awards the second solution separately — candidates who only give the principal value routinely drop that mark.

June 2023 Paper 1 mark scheme (general pattern)

Try it — exam-style

Easy

ORIGINAL · after June 2023 Paper 1 Q08

A sector has radius 8 cm and angle 1.2 radians. Find (i) the arc length and (ii) the area of the sector.

(3)

(Total for Question 1 is 3 marks)

Medium

ORIGINAL · after June 2024 Paper 1 Q12

Express

3\cos\theta - 4\sin\theta

in the form

R\cos(\theta + \alpha)

, where

R > 0

and

0 < \alpha < 90^\circ

. Hence state the maximum value of

3\cos\theta - 4\sin\theta

(4)

(Total for Question 2 is 4 marks)

Hard

ORIGINAL

Solve

2\sin^2 x + 3\cos x = 3

for

0^\circ \le x \le 360^\circ

(4)

(Total for Question 3 is 4 marks)

Medium

ORIGINAL · after June 2023 Paper 1 Q13

The height of a carriage on a wheel is modelled by

H = 12 - 10\cos(30t)^\circ

, with

H

in metres and

t

in minutes. State (i) the maximum height, (ii) the minimum height, and (iii) the time for one complete revolution.

(3)

(Total for Question 4 is 3 marks)

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

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Drill it properly

Formulae to Memorise

Exact trig values and the identities, with a recall drill.

Graph Transformations

How a - b cos(kt) is built from cos t, step by step.

Maths flashcards

Identities, exact values and sector formulas, on a schedule.

Stuck on trigonometry?

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