Question

$\sin {2025}^{\circ }$ is equal to

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

Answer 1

The correct option is B $-\frac{1}{\sqrt{2}}$

$\sin {2025}^{\circ }=\sin (11\times {180}^{\circ }+{45}^{\circ })=\sin (11\pi +{45}^{\circ })$
$(11\pi +{45}^{\circ })$ lies in 3rd quadrant, and $\sin$ of 3rd quadrant angle takes negative value.
$\therefore \sin (11\pi +{45}^{\circ })=-\sin {45}^{\circ }=-\frac{1}{\sqrt{2}}$