Question

If $tanx=-\frac{3}{4},\frac{3\pi }{2}<x<2\pi$, then find $\sin 2x$

Answer 1

In the given domain,

If $tanx=-\frac{3}{4}$,

Then,

$sinx=-\frac{3}{5}$ , $cosx=\frac{4}{5}$

$\Rightarrow$ $sin2x=2sinx.cosx$

$\Rightarrow$ $2\times (-\frac{3}{5})\times \frac{4}{5}$

$\Rightarrow$ $\frac{-24}{16}$