IB Maths AA HL 3.8 Trigonometric equations Question Bank

Practise IB Mathematics SL/HL 3.8 by applying trigonometric equations methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 5]

Solve $2 \sin \left(x+60^{\circ}\right)=\cos \left(x+30^{\circ}\right), 0^{\circ} \leq x \leq 180^{\circ}$ .

$\quad 2 \sin \left(x+60^{\circ}\right)=\cos \left(x+30^{\circ}\right)$ $2\left(\sin x \cos 60^{\circ}+\cos x \sin 60^{\circ}\right)=\cos x \cos 30^{\circ}-\sin x \sin 30^{\circ}$
(M1)(A1)
$2 \sin x \times \frac{1}{2}+2 \cos x \times \frac{\sqrt{3}}{2}=\cos x \times \frac{\sqrt{3}}{2}-\sin x \times \frac{1}{2}$ $\Rightarrow \frac{3}{2} \sin x=-\frac{\sqrt{3}}{2} \cos x$ $\Rightarrow \tan x=-\frac{1}{\sqrt{3}}$ $\Rightarrow x=150^{\circ}$

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SL 3.8—Trigonometric equations question 1