QuestionJuly 26, 2025

Solve the trigonometric equation for all values 0leqslant xlt 2pi 2sinx-sqrt (3)=0

Solve the trigonometric equation for all values 0leqslant xlt 2pi 2sinx-sqrt (3)=0
Solve the trigonometric equation for all values 0leqslant xlt 2pi 
2sinx-sqrt (3)=0

Solution
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Answer

x = \frac{\pi}{3}, \frac{2\pi}{3} Explanation 1. Isolate \sin x Add \sqrt{3} to both sides: 2\sin x = \sqrt{3}. 2. Solve for \sin x Divide by 2: \sin x = \frac{\sqrt{3}}{2}. 3. Find solutions in the given interval \sin x = \frac{\sqrt{3}}{2} at x = \frac{\pi}{3} and x = \frac{2\pi}{3} within 0 \leq x < 2\pi.

Explanation

1. Isolate $\sin x$<br /> Add $\sqrt{3}$ to both sides: $2\sin x = \sqrt{3}$.<br />2. Solve for $\sin x$<br /> Divide by 2: $\sin x = \frac{\sqrt{3}}{2}$.<br />3. Find solutions in the given interval<br /> $\sin x = \frac{\sqrt{3}}{2}$ at $x = \frac{\pi}{3}$ and $x = \frac{2\pi}{3}$ within $0 \leq x < 2\pi$.
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