document.write( "Question 1127103: Find the exact value of sin(a+b), given that sin a=-4/5 and cos b = 12/13, with a in quadrant III and b in quadrant IV \n" ); document.write( "
Algebra.Com's Answer #743457 by ikleyn(52794)\"\" \"About 
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document.write( "Use the formula \r\n" );
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document.write( "    sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b)    (1)\r\n" );
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document.write( "Regarding this formula, 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) = \"-4%2F5\"  and  cos(b) = \"12%2F13\", you need to know  cos(a) and sin(b).\r\n" );
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document.write( "1.  cos(a) = \"sqrt%281-sin%5E2%28a%29%29\" = \"sqrt%281+-+%28-4%2F5%29%5E2%29\" = \"sqrt%281+-+16%2F25%29\" = \"sqrt%28%2825-16%29%2F25%29\" = \"sqrt%289%2F25%29\" = -\"3%2F5\" =-\"3%2F5\".\r\n" );
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document.write( "   The sign \"-\" was chosen for the square root because cos(a) is negative when the angle \"a\" is in QIII.\r\n" );
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document.write( "2.  sin(b) = = \"sqrt%281-cos%5E2%28b%29%29\" = \"sqrt%281+-+%2812%2F13%29%5E2%29\" = \"sqrt%281+-+144%2F169%29\" = \"sqrt%28169-144%29%2F169%29\" = \"sqrt%2825%2F169%29\" = -\"5%2F13\".\r\n" );
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document.write( "   The sign \"-\" was chosen for the square root because sin(b) is negative when the angle \"b\" is in QIV.\r\n" );
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document.write( "Now all you need to do is to substitute everything into the formula (1) and make the calculations.\r\n" );
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document.write( "sin(a+b) = \"%28-4%2F5%29%2A%2812%2F13%29+%2B+%28-3%2F5%29%2A%28-5%2F13%29\" = \"-48%2F65+%2B+15%2F65\" = \"%28-48%2B15%29%2F65\" = \"-33%2F65\".     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "To see many other similar solved problems on calculating/evaluating trig functions,  look into the lessons \r
\n" ); document.write( "\n" ); document.write( "    - Calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "    - Evaluating trigonometric expressions \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Trigonometry: Solved problems\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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