Question

The value of $\left\{\sin \frac{25\pi }{3}\right\}$ is
(where $\{.\}$ is fractional part function)

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

Answer 1

The correct option is C $\frac{\sqrt{3}}{2}$

Given,
$\left\{\sin \frac{25\pi }{3}\right\}=\left\{\sin (8\pi +\frac{\pi }{3})\right\}=\left\{\sin \frac{\pi }{3}\right\}=\left\{\frac{\sqrt{3}}{2}\right\}=\frac{\sqrt{3}}{2}(\because 0<\frac{\sqrt{3}}{2}<1)$