Algebra.Com's Answer #849529 by ikleyn(52864)![\"\"](\"/images/stars/stars-13.gif\")  
You can put this solution on YOUR website!
.
\n" );
document.write( "Please help. Thank you in advance.\r
\n" );
document.write( "\n" );
document.write( "Given tan 𝛼 =7/24, 𝛼 in the third quadrant, sin 𝛽 =2/√13, 𝛽 in the second quadrant, find:
\n" );
document.write( "a) the quadrant containing 𝛼 + 𝛽
\n" );
document.write( "b) the quadrant containing 𝛼 - 𝛽
\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "\r\n" );
document.write( "Notice that 7^2 + 24^ = 625 = 25^2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, you may think that \r\n" );
document.write( "\r\n" );
document.write( " tan(a) =  in the third quadrant is  =  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "In other words, you may think that sin(a) =  , cos(a) =  .\r\n" );
document.write( "\r\n" );
document.write( " The signs at sin(a) and cos(a) do agree that \"a\" is in the third quadrant.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Next, you are given that sin(b) =  in the second quadrant; so, you can calculate \r\n" );
document.write( "\r\n" );
document.write( " cos(b) =  =  =  =  =  .\r\n" );
document.write( "\r\n" );
document.write( " The sign at cos(b) does agree that \"b\" is in the second quadrant.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now, as you know sin(a) , cos(a) = , sin(b) = , cos(b) = , you can calculate\r\n" );
document.write( "\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( "\r\n" );
document.write( "\r\n" );
document.write( " cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) =  -  =  -  = \r\n" );
document.write( "\r\n" );
document.write( " =  =  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus, sin(a+b) is a negative real number; cos(a+b) is a positive real number.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It means that angle a+b is in fourth quadrant.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER. Angle a+b is in fourth quadrant.\r\n" );
document.write( " \r
\n" );
document.write( "\n" );
document.write( "Part (a) is solved completely.\r
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( "For part (b), calculate sin(a-b) and cos(a-b) similarly; then make a conclusion about angle a-b.\r
\n" );
document.write( "\n" );
document.write( "You just have a TEMPLATE for it.\r
\n" );
document.write( "
\n" );
document.write( "
\n" );
document.write( "\n" );
document.write( " \n" );
document.write( " |