If $sinu=-4/5$ and $pi < u < (3pi)/2$ , find $sin2u,cos2u$ and $tan2u$ ?

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Answer 1 · 2017-08-22T12:08:06

$sin2u=24/25$ , $cos2u=-7/25$ and $tan2u=-24/7$

As $pi < u < (3pi)/2$ , $u$ is in $Q3$ and $cosu<0$ .

As $sinu=-4/5$ , $cosu=-sqrt(1-(-4/5)^2)=-3/5$

Hence, $sin2u=2sinucosu=2xx(-4/5)xx(-3/5)=24/25$

$cos2u=cos^2u-sin^2u=9/25-16/25=-7/25$

and $tan2u=(sin2u)/(cos2u)=(24/25)/(-7/25)=-24/7$

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