IB Maths AA HL Sl 3 8 Trigonometric Equations Questions

Practise solving trigonometric equations on finite intervals, retaining valid roots, checking branches and applying identities to periodic or physical models.

Exam points

Solve a basic sine, cosine or tangent equation on a finite interval and list every solution in the required degree/radian form.
Reduce an equation to a quadratic or other algebraic equation in sin x, cos x or tan x, then back-substitute and retain only interval-valid roots.
Use reciprocal or trig identities and factorisation to simplify a more complex equation before solving it, checking excluded denominators and branches.
Use a periodic equation or model to find times, positions, threshold intervals or solution counts in the stated physical context.

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Study SL 3.8—Trigonometric equations conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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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IB Maths AA HL Sl 3 8 Trigonometric Equations Questions question 1