If $sin u = - \frac{4}{5}$ $sinu=-4/5$ and $π < u < \frac{3 π}{2}$ $pi < u < (3pi)/2$ , find $sin 2 u, cos 2 u$ $sin2u,cos2u$ and $tan 2 u$ $tan2u$ ?

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Answer 1 · 2017-08-22T12:08:06

$sin 2 u = \frac{24}{25}$ $sin2u=24/25$ , $cos 2 u = - \frac{7}{25}$ $cos2u=-7/25$ and $tan 2 u = - \frac{24}{7}$ $tan2u=-24/7$

As $π < u < \frac{3 π}{2}$ $pi < u < (3pi)/2$ , $u$ $u$ is in $Q 3$ $Q3$ and $cos u < 0$ $cosu<0$ .

As $sin u = - \frac{4}{5}$ $sinu=-4/5$ , $cos u = - \sqrt{1 - {(- \frac{4}{5})}^{2}} = - \frac{3}{5}$ $cosu=-sqrt(1-(-4/5)^2)=-3/5$

Hence, $sin 2 u = 2 sin u cos u = 2 \times (- \frac{4}{5}) \times (- \frac{3}{5}) = \frac{24}{25}$ $sin2u=2sinucosu=2xx(-4/5)xx(-3/5)=24/25$

$cos 2 u = {cos}^{2} u - {sin}^{2} u = \frac{9}{25} - \frac{16}{25} = - \frac{7}{25}$ $cos2u=cos^2u-sin^2u=9/25-16/25=-7/25$

and $tan 2 u = \frac{sin 2 u}{cos 2 u} = \frac{\frac{24}{25}}{- \frac{7}{25}} = - \frac{24}{7}$ $tan2u=(sin2u)/(cos2u)=(24/25)/(-7/25)=-24/7$

If sinu=−45sinu=-4/5 and π<u<3π2pi < u < (3pi)/2, find sin2u,cos2usin2u,cos2u and tan2utan2u?