document.write( "Question 921735: If sin p=3/5 and tan q=5/12, find the exact value of sin (p-q). (p and q are acute angles) Thorough steps and details to the answer, please. \n" ); document.write( "
Algebra.Com's Answer #559233 by lwsshak3(11628)\"\" \"About 
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If sin p=3/5 and tan q=5/12, find the exact value of sin (p-q). (p and q are acute angles) Thorough steps and details to the answer, please.
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\n" ); document.write( "sin p=3/5
\n" ); document.write( "cos p=4/5 (working with a (3-4-5) reference right triangle in quadrant I.)
\n" ); document.write( "tan q=5/12(working with a (5-12-13) reference right triangle in quadrant I.)
\n" ); document.write( "sin q=5/13
\n" ); document.write( "cos q=12/13
\n" ); document.write( "..
\n" ); document.write( "Identity: sin(x-y)=sinxcosy-cosxsiny
\n" ); document.write( "sin(p-q)=(sin p*cos q)-(cos p*sin q)=(3/5*12/13)-(4/5*5/13)=36/65-20/65=16/65
\n" ); document.write( "..
\n" ); document.write( "Calculator check:
\n" ); document.write( "sin p=3/5
\n" ); document.write( "p≈36.87˚
\n" ); document.write( "tan q=5/12
\n" ); document.write( "q=22.62˚
\n" ); document.write( "p-q=36.87-22.62≈14.25˚
\n" ); document.write( "sin(p-q)=sin (14.25˚)≈0.2462
\n" ); document.write( "Exact value=16/65≈0.2462 \n" ); document.write( "
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