Edexcel A-Level Mathematics A2 P3.2 Trigonometry Questions

Practise P3 trigonometry by rewriting equations with identities, solving within intervals and using Rcos or Rsin forms in calculus contexts.

Exam points

rewrite equations using sec, cosec, cot and double-angle identities before solving
express a cos x + b sin x in Rcos(x+α) form, giving exact R and rounded α
solve trigonometric equations on a stated interval, rejecting impossible or extra roots

Covered syllabus points

P3.2.1 - Secant, cosecant and cotangent P3.2.2 - Further trigonometric identities P3.2.3 - Knowledge

[Maximum number: 1]

A curve C has equation y=f(x), where

f(x)=\arcsin\left(\frac{x}{2}\right),\qquad -2\leqslant x\leqslant2,\qquad -\frac{\pi}{2}\leqslant y\leqslant\frac{\pi}{2}

Sketch C.

[Maximum number: 4]

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

Show that the equation

$2\sin\theta(3\cot^2 2\theta-7)=13\sec\theta$

can be written as

$3\operatorname{cosec}^2 2\theta-13\operatorname{cosec}2\theta-10=0$

$3\cot^2 2\theta-7=\frac{13}{2\sin\theta\cos\theta}$ $3(\operatorname{cosec}^2 2\theta-1)-7=\frac{13}{2\sin\theta\cos\theta}$ $3\operatorname{cosec}^2 2\theta-10=13\operatorname{cosec}2\theta$ $3\operatorname{cosec}^2 2\theta-13\operatorname{cosec}2\theta-10=0$

M1 dM1 ddM1 A1*

[Maximum number: 2]

Using the identity for $\cos (A+B)$ , prove that

\cos 2 A \equiv 2 \cos ^{2} A-1

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Covered syllabus points

Question 1

Question 2

Question 3