Pearson Edexcel IAL Mathematics P2.6 Trigonometry Question Bank

Practise rewriting trigonometric expressions with identities, then solving equations over stated degree or radian intervals with exact or rounded answers.

[Maximum number: 8]

In this question you must show detailed reasoning.

Solutions relying entirely on calculator technology are not acceptable.

(a)

Show that the equation

(3 \cos \theta-\tan \theta) \cos \theta=2

can be written as

3 \sin ^{2} \theta+\sin \theta-1=0

[ 3 ]

$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow \cos \theta\left(3 \cos \theta-\frac{\sin \theta}{\cos \theta}\right)=2$

or e.g.
$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow 3 \cos ^{2} \theta-\sin \theta=2$

or e.g.
$\cos \theta(3 \cos \theta-\tan \theta)=2 \Rightarrow 3 \cos ^{2} \theta-\frac{\sin \theta}{\cos \theta} \cos \theta=2$

M1

$3\left(1-\sin ^{2} \theta\right)-\sin \theta=2$

M1

$3 \sin ^{2} \theta+\sin \theta-1=0 *$

A1*

(3)

(b)

Hence solve for $-\frac{\pi}{2} \leqslant x \leqslant \frac{\pi}{2}$

(3 \cos 2 x-\tan 2 x) \cos 2 x=2

[ 5 ]

Solving the quadratic from part (a) gives
$\sin 2x=\frac{-1\pm\sqrt{13}}{6}$
or approximately 0.434 and -0.768.
Then solve $2x=\sin^{-1}(0.434)$ or $2x=\sin^{-1}(-0.768)$ in the range $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$ .
x=-1.13, -0.438, 0.225, 1.35.
M1 A1 M1 A1 A1

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Pearson Edexcel IAL Mathematics P2.6 Trigonometry Question Bank

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P2.6 - Trigonometry question 1

Question (a)

Question (b)