Edexcel IAL P3 Trigonometric Addition Formulae Questions
Addition and double-angle formulae; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α).
- P3 · Pure Mathematics 3
- Calculator allowed
- 34 practice questions
What the questions test
The 34 P3 trigonometric addition formulae practice questions cover:
Worked example 1
Solve the equation \(\cos 2x = \sin x\) for \(-\pi \le x \le \pi\). Give your answers as exact radian values.
Mark scheme
Substitute the double angle identity \(\cos 2x = 1 - 2\sin^2 x\). M1
\(1 - 2\sin^2 x = \sin x \implies 2\sin^2 x + \sin x - 1 = 0\). A1
Factorise the quadratic: \((2\sin x - 1)(\sin x + 1) = 0\). M1A1
Case 1: \(2\sin x - 1 = 0 \implies \sin x = \frac{1}{2}\).
Within the domain \(-\pi \le x \le \pi\), solutions are \(x = \frac{\pi}{6}\) and \(x = \frac{5\pi}{6}\). A1
Case 2: \(\sin x + 1 = 0 \implies \sin x = -1\).
Within the domain \(-\pi \le x \le \pi\), the solution is \(x = -\frac{\pi}{2}\). A1
Worked example 2
Solve the equation $\tan 2x = 4\tan x$ for $0^\circ \le x \le 180^\circ$. Give your answers to 1 decimal place where appropriate.
Mark scheme
- M1 for substituting the identity $\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$.
- M1 for rearranging to $2\tan x = 4\tan x (1 - \tan^2 x)$.
- M1 for grouping terms on one side and factorising to get $2\tan x(2\tan^2 x - 1) = 0$.
- A1 for finding solutions from $\tan x = 0$, giving $x = 0^\circ$ and $180^\circ$.
- A1 for finding solutions from $\tan^2 x = 0.5 \implies \tan x = \pm \frac{1}{\sqrt{2}}$, giving $x = 35.3^\circ$ and $x = 144.7^\circ$.
FAQ
What trigonometric addition formulae is in Edexcel IAL P3?
Addition and double-angle formulae; a cos θ + b sin θ in the form R cos(θ ± α) or R sin(θ ± α).
Is P3 a calculator paper?
Yes, a calculator is allowed in P3, but method marks are only given for working you write down.
How are P3 trigonometric addition formulae questions marked?
With M marks for a correct method, A marks for accurate answers that depend on the M mark before them, and B marks for independent results, as in the worked examples on this page.