Q60 / 160 · AP EAMCET 2022 (05 Jul Shift 1) · Mathematics

If $\sin \theta=-\frac{3}{4}$, then $\sin 2 \theta=$

  • A
    $\frac{3 \sqrt{7}}{8}$
  • Correct answer
    B
    $-\frac{3 \sqrt{7}}{8}$
  • C
    $\frac{2 \sqrt{3}}{7}$
  • D
    $-\frac{2 \sqrt{3}}{7}$

Solution

If $\sin \theta=\frac{-3}{4}$ $\begin{aligned} & \cos \theta=\sqrt{1-\sin ^2 \theta} \\ & \cos \theta=\sqrt{1-\left(\frac{-3}{4}\right)^2} \\ & \cos \theta=\sqrt{\frac{16-9}{4}}=\sqrt{\frac{7}{16}}\end{aligned}$ $\therefore \sin 2 \theta=2 \sin \theta \cdot \cos \theta$ $=2 \times\left(\frac{-3}{4}\right)\left(\frac{\sqrt{7}}{4}\right)=\frac{-3 \sqrt{7}}{8}$

Hence, the correct answer is option: 'B'.

Relevant Questions