Question

Given $\cos \theta =\frac{\sqrt{3}}{2}$, which of the following are the possible values of $\sin 2\theta$?

• A. $\frac{\sqrt{3}}{2}$
• B. $-\frac{1}{2}$
• C. $1$
• D. $0$

Answer 1

Answer: (A)

$\frac{\sqrt{3}}{2}$

$\sin 2\theta =2\sin \theta \cos \theta =2\sqrt{1-{\cos }^2\theta }\cos \theta$

$=2\times \frac{1}{2}\times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{2}$.