document.write( "Question 1056959: let sinA= 3/5 with A in Q2 and sinB= -5/13 with b in quadrant 3. find sin(A+B), cos(a+b), and tan(a+b). where does a and b terminate \n" ); document.write( "
Algebra.Com's Answer #672033 by ikleyn(52799)\"\" \"About 
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\n" ); document.write( "let sinA= 3/5 with A in Q2 and sinB= -5/13 with B in quadrant 3. find sin(A+B), cos(a+b), and tan(a+b). where does a and b terminate
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document.write( "Use the formulas \r\n" );
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document.write( "\"sin%28alpha%2Bbeta%29\" = \"sin%28alpha%29%2Acos%28beta%29+%2B+cos%28alpha%29%2Asin%28beta%29\"    (1)\r\n" );
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document.write( "   and\r\n" );
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document.write( "\"cos%28alpha%2Bbeta%29\" = \"cos%28alpha%29%2Acos%28beta%29+-+sin%28alpha%29%2Asin%28beta%29\".   (2)\r\n" );
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document.write( "Regarding these formulas, see the lesson Addition and subtraction formulas in this site.\r\n" );
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document.write( "In addition to the given  sin(A) = \"3%2F5\"  and  sin(B) = \"-5%2F13\", you need to know  cos(A) and cos(B).\r\n" );
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document.write( "1.  cos(A) = \"sqrt%281-sin%5E2%28A%29%29\" = \"-sqrt%281+-+%283%2F5%29%5E2%29\" = \"-sqrt%281+-+9%2F25%29\" = \"-sqrt%28%2825-9%29%2F25%29\" = \"-sqrt%2816%2F25%29\" = \"-4%2F5\".\r\n" );
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document.write( "   The sign \"-\" was chosen for the square root because cosine is negative in Q2.\r\n" );
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document.write( "2.  cos(B) = = \"-sqrt%281-sin%5E2%28B%29%29\" = \"-sqrt%281+-+%28-5%2F13%29%5E2%29\" = \"-sqrt%281+-+25%2F169%29\" = \"-sqrt%28%28169-25%29%2F169%29\" = \"-sqrt%28144%2F169%29\" =\"-12%2F13\" = \"-12%2F13\".\r\n" );
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document.write( "   The sign \"-\" was chosen for the square root because cosine is negative in Q3.\r\n" );
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document.write( "Now all you need to do is to substitute everything into the formulas (1) and (2) and make the calculations.\r\n" );
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document.write( "\"sin%28A%2BB%29\" = \"%283%2F5%29%2A%28-12%2F13%29+%2B+%28-4%2F5%29%2A%285%2F13%29\" = \"-36%2F65+-+20%2F65\" = \"%28-36-20%29%2F65\" = \"-56%2F65\",   and\r\n" );
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document.write( "\"cos%28A%2BB%29\" = \"%28-4%2F5%29%2A%28-12%2F13%29+-+%283%2F5%29%2A%28-5%2F13%29\" = \"48%2F65+%2B+15%2F65\" = \"%2848%2B15%29%2F65\" = \"63%2F65\".\r\n" );
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document.write( "Finally, tan(A+B) = \"sin%28A%2BB%29%2Fcos%28A%2BB%29\" = \"%28%28-56%2F65%29%29%2F%28%2863%2F65%29%29\" = \"-56%2F63\".\r\n" );
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\n" ); document.write( "\n" ); document.write( "The last question \"where does a and b terminate\" is just answered in your condition.\r
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