document.write( "Question 1117291: 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 #732325 by ikleyn(52915)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "
\r\n" );
document.write( "Use the formula\r\n" );
document.write( "\r\n" );
document.write( "sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B).     (*)\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For it, in addition to the given values  sin(A) = \"4%2F5\" and cos(B) = \"-5%2F13\"  you need to find  cos(A)  and  sin(B).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "1.  Since sin(A) = \"4%2F5\",  cos(A) = \"sqrt%281+-+sin%5E2%28A%29%29\" = \"sqrt%281-%284%2F5%29%5E2%29\" = \"sqrt%281-16%2F25%29\" = \"sqrt%2825-16%29%2F25%29\" = \"sqrt%289%2F25%29\" = \"3%2F5%29\".\r\n" );
document.write( "\r\n" );
document.write( "    Notice that cos(A) is positive in QI.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  Since cos(B) = \"-5%2F13\",  sin(B) = \"sqrt%281+-+cos%5E2%28B%29%29\" = \"sqrt%281-%28-5%2F13%29%5E2%29\" = \"sqrt%281-25%2F169%29\" = \"sqrt%28169-25%29%2F169%29\" = \"sqrt%28144%2F169%29\" = \"12%2F13%29\".\r\n" );
document.write( "\r\n" );
document.write( "    Notice that sin(B) is positive in QII.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  Now you have everything to use the formula (*). Substitute all given and found values into (*). You will get  \r\n" );
document.write( "\r\n" );
document.write( "    sin(A-B) = sin(A)*cos(B) - cos(A)*sin(B) = \"%284%2F5%29%2A%28-5%2F13%29+-+%283%2F5%29%2A%2812%2F13%29\" = \"-20%2F65+-+36%2F65\" = \"-56%2F65\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.   sin(A-B) = \"-56%2F65\".\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "---------------
\n" ); document.write( "To see many other similar solved problems, 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
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Trigonometry: Solved problems\". \r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
\n" ); document.write( "
\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
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );