document.write( "Question 955463: Find sin 2x, cos 2x, and tan 2x from the given information.
\n" ); document.write( "csc x = 7, tan x < 0
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Algebra.Com's Answer #583709 by lwsshak3(11628)\"\" \"About 
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Find sin 2x, cos 2x, and tan 2x from the given information.
\n" ); document.write( "csc x = 7, tan x < 0
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\n" ); document.write( "Reference angle x is in quadrant II where sin>0, cos<0
\n" ); document.write( "sinx=1/cscx=1/7
\n" ); document.write( "cosx=-√1-sin^2(x)=-√(1-1/49)=-√(48/49)=-(√48)/7
\n" ); document.write( "sin2x=2*sinx*cosx=2*1/7*-√48/7=-2*√48/49
\n" ); document.write( "cos2x=cos^2(x)-sin^2(x)=48/49-1/49=47/49
\n" ); document.write( "tan2x=sin2x/cos2x=-2√48/47
\n" ); document.write( "Check:
\n" ); document.write( "w/calculator:
\n" ); document.write( "sinx=1/7
\n" ); document.write( "x≈171.79˚
\n" ); document.write( "2x≈343.5736˚
\n" ); document.write( "tan2x≈tan(343.57)≈-0.2948
\n" ); document.write( "exact value as computed=-2√48/47≈-0.2948 \n" ); document.write( "
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