Question 873905
Use the given information to find cos 2x, sin 2x, and tan 2x. (Enter your answers in exact form.)
sin x = (SQRT Root 3/ 5) , &#960;/2 < x < &#960;
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{{{sinx=sqrt(3)/5}}}
{{{cosx=-sqrt(1-sin^2(x))=-sqrt(1-3/25)=-sqrt(22/25)=-sqrt(22)/5}}}
{{{tanx=(sinx/cosx)=-sqrt(3/22)}}}
...
{{{cos(2x)=cos^2(x)-sin^2(x)=22/25-3/25=19/25}}}
{{{sin(2x)=2sin(x)cos(x)=2*(sqrt(3)/5)*(-sqrt(22)/5)=-2sqrt(66)/25}}}
{{{tan(2x)=2tan(x)/(1-tan^2(x))=-2sqrt(3/22)/(1-3/22)=-2sqrt(3/22)/(19/22)=-2sqrt(3/22)*(22/19)}}}