Solve the equation sin 2x=sqrt3/2 for x in the interval 0le xle 2pi.

Solve the equation $s in 2 x = \frac{s q r t 3}{2}$ for $x$ in the interval $0 l e x l e 2 p i$ .

medium 2 marks Class 11 · Mathematics · Trigonometric Functions

Answer

\displaystyle \left{\frac{\pi}{6},,\frac{\pi}{3},,\frac{7\pi}{6},,\frac{4\pi}{3}\right}

The correct answer is $\displaystyle \left{\frac{\pi}{6},,\frac{\pi}{3},,\frac{7\pi}{6},,\frac{4\pi}{3}\right}$ — Thus $x = \frac{p i}{6},; \frac{p i}{3},; \frac{7 p i}{6},; \frac{4 p i}{3}$ .

Step-by-step solution

Set $s in 2 x = \frac{s q r t 3}{2}$ .
Recognise that $s in θ = \frac{3}{2}$ when $θ = \frac{π}{3} + 2 k p i$ or $θ = \frac{2 π}{3} + 2 k p i$ , $k inma t hbb Z$ .
Replace $θ$ by $2 x$ : $2 x = \frac{π}{3} + 2 k p i$ or $2 x = \frac{2 π}{3} + 2 k p i$ .
Divide by $2$ : $x = \frac{p i}{6} + k p i$ or $x = \frac{p i}{3} + k p i$ .
Choose $k = 0$ and $k = 1$ to keep $x$ in $[0, 2 p i]$ .
Thus $x = \frac{p i}{6},; \frac{p i}{3},; \frac{7 p i}{6},; \frac{4 p i}{3}$ .

Common mistake: Forgetting one set of solutions or missing the

2 p i

periodicity of

s in 2 x

Concept tested: Solving trigonometric equations

Published 1 October 2026 · How this solution was prepared and checked

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Solve the equation sin2x=2sqrt3​ for x in the interval 0lexle2pi.

Step-by-step solution

Solve the equation $s in 2 x = \frac{s q r t 3}{2}$ for $x$ in the interval $0 l e x l e 2 p i$ .