document.write( "Question 867728: tan β = 2, 180° < β < 270°. Find the exact value of sin 2β and cos 2β \n" ); document.write( "

Algebra.Com's Answer #523232 by lwsshak3(11628) $\"\"$ $\"About$

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tan β = 2, 180° < β < 270°. Find the exact value of sin 2β and cos 2β
\n" ); document.write( "hypotenuse of reference right triangle= $\"sqrt%282%5E2%2B1%5E2%29=sqrt%284%2B1%29=sqrt%285%29\"$
\n" ); document.write( " $\"cos%28beta%29=-1%2Fsqrt%285%29\"$
\n" ); document.write( " $\"sin%28beta%29=-2%2Fsqrt%285%29\"$
\n" ); document.write( "

\n" ); document.write( " $\"cos%282beta%29=cos%5E2%28beta%29-sin%5E2%28beta%29=1%2F5-4%2F5=-3%2F5\"$
\n" ); document.write( "..
\n" ); document.write( "Calculator check:
\n" ); document.write( "tan(B)=2
\n" ); document.write( "B=243.435(in quadrant III)
\n" ); document.write( "2B≈486.87(in quadrant II)
\n" ); document.write( "sin(2B)=sin(486.87)≈0.7999…
\n" ); document.write( "Exact value as calculated=4/5=0.8000
\n" ); document.write( "cos(2B)=cos(486.87≈-0.6000…
\n" ); document.write( "Exact value as calculated=-3/5=-0.6000 \n" ); document.write( "

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