Question

Evaluate the following $\sin (-\frac{25\pi }{4})$.

Answer 1

Evaluate the following $\sin (-\frac{25\pi }{4})$

Here We are given, $\sin (-\frac{25\pi }{4})$

$=\sin (-\frac{24\pi -\pi }{4})$

$=\sin (-6\pi -\frac{\pi }{4})$

$=\sin [-1(6\pi +\frac{\pi }{4})]$

$=-\sin \left(6\pi \frac{\pi }{4}\right)$

as $\sin$ function is odd functions

$=-\sin \left(\frac{\pi }{4}\right)$

$[as\theta =6\pi +\frac{\pi }{4}isinFirstQuadrantSo,the\sin \theta willnotchangeas\theta =\pi /4]$

$=-(-\frac{1}{\sqrt{2}})$

$=\frac{-1}{\sqrt{2}}$

So, $\sin \left(\frac{-25\pi }{4}\right)=\frac{-1}{\sqrt{2}}$