- \sqrt{3}
-\frac{\sqrt{3}}{2}
\frac{\sqrt{3}}{2}
\sqrt{3}
Correct answer is A
\sin \theta = \frac{\sqrt{3}}{2} \implies opp = \sqrt{3}; hyp = 2
adj^{2} = 2^{2} - (\sqrt{3})^{2} = 1 \implies adj = 1
\cos \theta = \frac{1}{2}
\sin 2\theta = \sin (180 - \theta) = \sin \theta = \frac{\sqrt{3}}{2}
\cos 2\theta = \cos (180 - \theta) = -\cos \theta = -\frac{1}{2}
\tan 2\theta = \frac{\sin 2\theta}{\cos 2\theta} = \frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}
= - \sqrt{3}
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