document.write( "Question 741621: Find sin (s+t) and cos (s+t) where sin(s)=3/5 and sin(t)=-12/13,in quadrant 1 and t in quadrant 3 \n" ); document.write( "

Algebra.Com's Answer #452098 by lwsshak3(11628) $\"\"$ $\"About$

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Find sin (s+t) and cos (s+t) where sin(s)=3/5 and sin(t)=-12/13, s in quadrant 1 and t in quadrant 3
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\n" ); document.write( " $\"cos%28s%29=sqrt%281-sin%5E2%28s%29%29=sqrt%281-9%2F25%29=sqrt%2816%2F25%29=4%2F5\"$ (in quadrant 1 where cos>0)
\n" ); document.write( " $\"cos%28t%29=sqrt%281-sin%5E2%28t%29%29=sqrt%281-144%2F169%29=sqrt%2825%2F169%29=-5%2F13\"$ (in quadrant 3 where cos<0)
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\n" ); document.write( "sin(s+t)=sin(s)cos(t)+cos(s)sin(t)=3/5*-5/13+4/5*-12/13=-15/65-48/65=-63/65
\n" ); document.write( "cos(s+t)=cos(s)cos(t)-sin(s)sin(t)=4/5*-5/13-3/5*-12/13=-20/65+36/65=16/65
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\n" ); document.write( "Calculator check:
\n" ); document.write( "sin(s)=3/5
\n" ); document.write( "s≈36.87º
\n" ); document.write( "sin(t)=-12/13
\n" ); document.write( "t≈247.38
\n" ); document.write( "s+t≈284.25º
\n" ); document.write( "..
\n" ); document.write( "sin(s+t)=sin(284.25º)≈-0.9692..
\n" ); document.write( "as computed,-63/65≈-0.9692..
\n" ); document.write( "..
\n" ); document.write( "cos(s+t)≈cos(284.25º)≈0.2461..
\n" ); document.write( "as computed,16/65≈0.2461.. \n" ); document.write( "

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