document.write( "Question 924283: Sin A = \"+sqrt+%285%29+%2F+3+\" and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A \n" ); document.write( "
Algebra.Com's Answer #560940 by lwsshak3(11628)\"\" \"About 
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Sin A = \"+sqrt+%285%29+%2F+3+\" and the measure of angle A is in Quadrant I . Find, in the simplest form , the value of sin2A and cos2A
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\n" ); document.write( "use x for A
\n" ); document.write( "sinx=√5/3
\n" ); document.write( "cosx=√(1-sin^2(x))=√(1-5/9)=√(4/9)=2/3
\n" ); document.write( "sin(2x)=2sinxcosx=2*√5/3*2/3=4√5/9
\n" ); document.write( "cos 2x=cos^2(x)-sin^2(x)=4/9-5/9=-1/9
\n" ); document.write( "..
\n" ); document.write( "check:
\n" ); document.write( "sinx=√5/3
\n" ); document.write( "x=48.19
\n" ); document.write( "2x=96.38˚
\n" ); document.write( "..
\n" ); document.write( "sin(2x)≈sin(96.38)≈0.9938 (from calculator)
\n" ); document.write( "exact value as computed=4√5/9≈0.9938
\n" ); document.write( "..
\n" ); document.write( "cos(2x)=cos(96.38)≈-0.1111(from calculator)
\n" ); document.write( "exact value as computed=-1/9≈-0.1111
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