AP EAMCET · Maths · Trigonometric Ratios & Identities
If \(\sin \theta=-\frac{3}{4}\), then \(\sin 2 \theta=\)
- A \(\frac{3 \sqrt{7}}{8}\)
- B \(-\frac{3 \sqrt{7}}{8}\)
- C \(\frac{2 \sqrt{3}}{7}\)
- D \(-\frac{2 \sqrt{3}}{7}\)
Answer & Solution
Correct Answer
(B) \(-\frac{3 \sqrt{7}}{8}\)
Step-by-step Solution
Detailed explanation
If \(\sin \theta=\frac{-3}{4}\) \(\begin{aligned} & \cos \theta=\sqrt{1-\sin ^2 \theta} \\ & \cos \theta=\sqrt{1-\left(\frac{-3}{4}\right)^2} \\ & \cos \theta=\sqrt{\frac{16-9}{4}}=\sqrt{\frac{7}{16}}\end{aligned}\) \(\therefore \sin 2 \theta=2 \sin \theta \cdot \cos \theta\)…
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