document.write( "Question 958899: how do i find the exact value of sin(tan^-1 3/8) without using a calculator? \n" ); document.write( "
Algebra.Com's Answer #586034 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "sin[tan-1(3/8)]\r\n" );
document.write( "\r\n" );
document.write( "This says \"Find the sin of the angle whose tangent is 3/8\"\r\n" );
document.write( "\r\n" );
document.write( "So we sketch a right triangle that has an angle whose\r\n" );
document.write( "tangent is 3/8.\r\n" );
document.write( "\r\n" );
document.write( "Since the tangent is the opposite over the adjacent, and\r\n" );
document.write( "3/8 is 3 over 8, we the opposite side as 3, and the adjacent\r\n" );
document.write( "side as 8.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "The angle marked with the red arc is tan-1(3/8),\r\n" );
document.write( "the angle whose tangent is 3/8.\r\n" );
document.write( "\r\n" );
document.write( "Now we just need the sine of that angle marked.  (Its tangent is 3/8.)\r\n" );
document.write( "\r\n" );
document.write( "Since the sine is the opposite over the hypotenuse, we will need\r\n" );
document.write( "to find the hypotenuse:\r\n" );
document.write( "\r\n" );
document.write( "We use the Pythagorean theorem:\r\n" );
document.write( "\r\n" );
document.write( "\"hypotenuse%5E2=adjacent%5E2%2Bopposite%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"hypotenuse%5E2=8%5E2%2B3%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"hypotenuse%5E2=64%2B9\"\r\n" );
document.write( "\r\n" );
document.write( "\"hypotenuse%5E2=73\"\r\n" );
document.write( "\r\n" );
document.write( "\"hypotenuse=sqrt%2873%29\"\r\n" );
document.write( "\r\n" );
document.write( "So now we can label the hypotenuse:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now since the original problem is\r\n" );
document.write( "\r\n" );
document.write( "sin[tan-1(3/8)]\r\n" );
document.write( "\r\n" );
document.write( "We find the sine by putting the opposite side 3 over the hypotenuse √73\r\n" );
document.write( "\r\n" );
document.write( "So the answer is \r\n" );
document.write( "\r\n" );
document.write( "sin[tan-1(3/8)] = 3/√73\r\n" );
document.write( "\r\n" );
document.write( "If you like you can rationalize the denominator and get 3√73/73\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );