document.write( "Question 867571: Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
\n" ); document.write( "cos(u) = −1/7,pi/2\n" ); document.write( "

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Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.
\n" ); document.write( "cos(u) = −1/7,pi/2
\n" ); document.write( "***
\n" ); document.write( "Interval: [0,3π/2]
\n" ); document.write( "cos(u)=-1/7 (In quadrant II)
\n" ); document.write( " $\"sin%28u%29=sqrt%281-cos%5E2%28u%29%29=sqrt%281-1%2F49%29=sqrt%2848%2F49%29=sqrt%2848%29%2F7\"$
\n" ); document.write( "tan(u)=sin(u)/cos(u)=√48/-1=-√48
\n" ); document.write( "...
\n" ); document.write( "sin(2u)=2sin(u)cos(u)=2√48/7*(-1/7)=-(2√48)/49
\n" ); document.write( "cos(2u)=cos^2(u)-sin^2(u)=1/49-48/49=-47/49
\n" ); document.write( "tan(2u)=2tan(u)/1-tan^2(u)=-2√48/(1-48)=2√48/47
\n" ); document.write( "..
\n" ); document.write( "Calculator check:
\n" ); document.write( "cos(u)=-1/7
\n" ); document.write( "u≈98.21˚
\n" ); document.write( "2u≈196.42˚
\n" ); document.write( "...
\n" ); document.write( "sin(2u)≈sin(196.42)≈-0.2827…
\n" ); document.write( "Exact value=-(2√48)/49≈-0.2827…
\n" ); document.write( "..
\n" ); document.write( "cos(2u)≈cos(196.42)≈-0.9591…
\n" ); document.write( "Exact value=-47/49≈-0.9591…
\n" ); document.write( "..
\n" ); document.write( "tan(2u)≈tan(196.42)≈-0.2948…
\n" ); document.write( "Exact value=-(2√48)/47≈-0.2948…
\n" ); document.write( " \n" ); document.write( "

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