document.write( "Question 825963: If cos x = −4/5 and x is in quadrant II, ﬁnd cos 2x and sin 2x. \n" ); document.write( "

Algebra.Com's Answer #497851 by lwsshak3(11628) $\"\"$ $\"About$

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If cos x = −4/5 and x is in quadrant II, ﬁnd cos 2x and sin 2x.
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\n" ); document.write( "cosx=-4/5(working with (3-4-5) reference right triangle in quadrant II in which cos<0, sin>0)
\n" ); document.write( "sinx=3/5
\n" ); document.write( "sin2x=2sinxcosx=2*3/5*(-4/5)=-24/5
\n" ); document.write( "cos2x=cos^2x-sin^2x=16/25-9/25=7/25
\n" ); document.write( "..
\n" ); document.write( "calculator check:
\n" ); document.write( "cosx=-4/5 (in quadrant II)
\n" ); document.write( "x≈142.13˚
\n" ); document.write( "2x≈286.26˚
\n" ); document.write( "..
\n" ); document.write( "cos2x≈cos(286.26)≈0.2799..
\n" ); document.write( "Exact value=7/25≈0.28
\n" ); document.write( "..
\n" ); document.write( "sin2x≈sin(286.26)≈-0.9600..
\n" ); document.write( "Exact value=-24/25≈-0.9600 \n" ); document.write( "

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