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 trigonometric equations analytically or graphically on a stated finite interval, selecting all valid roots in the required degree or radian measure.
Reduce equations in sin x, cos x or tan x to quadratic form where appropriate, then verify the solution set against the interval and reject extraneous roots.

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