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Trigonometrical Equations
easy
Find the principal solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$
A
$\frac{\pi}{3}$ and $\frac{2 \pi}{3}$
B
$\frac{\pi}{3}$ and $\frac{2 \pi}{3}$
C
$\frac{\pi}{3}$ and $\frac{2 \pi}{3}$
D
$\frac{\pi}{3}$ and $\frac{2 \pi}{3}$
Solution
We know that, $\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$ and $\sin \frac{2 \pi}{3}=\sin \left(\pi-\frac{\pi}{3}\right)=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$
Therefore, principal solutions are $x=\frac{\pi}{3}$ and $\frac{2 \pi}{3}$.
Standard 11
Mathematics
