document.write( "Question 856628: find sin2x, cos2x, and tan2x if sinx= $\"-2%2Fsqrt%285%29\"$ and x terminates in quadrant III \n" ); document.write( "

Algebra.Com's Answer #516455 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
find sin2x, cos2x, and tan2x if sinx= $\"-2%2Fsqrt%285%29\"$ and x terminates in quadrant III
\n" ); document.write( "cos(x)=-√(1-sin^2(x))=-√(1-4/5)=-√(1/5)=-1/√5
\n" ); document.write( "tan(x)=sin(x)/cos(x)=-1/-2=1/2
\n" ); document.write( "..
\n" ); document.write( "sin(2x)=2sin(x)cos(x)=2*-2/√5*-1/√5=4/5
\n" ); document.write( "cos(2x)=cos^2x-sin^2(x)=(1/5)-4/5=-3/5
\n" ); document.write( "tan(2x)=2tan(x)/(1-tan^2(x))=2*(1/2)/(1-(1/2)^2)=1/(3/4)=4/3
\n" ); document.write( "..
\n" ); document.write( "Calculator check:
\n" ); document.write( "sinx=-2/√5
\n" ); document.write( "x≈243.43˚
\n" ); document.write( "2x≈486.87
\n" ); document.write( "sin(2x)≈sin(486.87)≈0.7999…
\n" ); document.write( "Exact value=4/5=0.8000
\n" ); document.write( "..
\n" ); document.write( "cos(2x)=cos(486.87)≈-0.6000…
\n" ); document.write( "Exact value=-3/5=-0.6000
\n" ); document.write( "..
\n" ); document.write( "tan(2x)=tan(486.87)≈-1.3333…
\n" ); document.write( "Exact value=4/3≈1.3333… \n" ); document.write( "

\n" );