document.write( "Question 1137999: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β). \n" ); document.write( "
Algebra.Com's Answer #755888 by ikleyn(52864)\"\" \"About 
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\n" ); document.write( "If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find sin(α - β).
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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) = \"-5%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+-+%284%2F5%29%5E2%29\" = \"sqrt%281+-+16%2F25%29\" = \"sqrt%28%2825-16%29%2F25%29\" = \"sqrt%289%2F25%29\" = \"3%2F5\".\r\n" );
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document.write( "        The sign \"+\" was chosen at the square root because the angle \"a\" is in QI.\r\n" );
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document.write( "    2.  sin(b) = \"sqrt%281-cos%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\".\r\n" );
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document.write( "        The sign \"+\" was chosen at the square root because sin(b) is positive when the angle \"b\" is in QII.\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) = \"%284%2F5%29%2A%28-5%2F13%29+-+%283%2F5%29%2A%2812%2F13%29\" = \"-15%2F65+-+36%2F65\" = \"%28-15-36%29%2F65\" = \"-51%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
\n" ); document.write( "\n" ); document.write( "in this site.\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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