document.write( "Question 577631: What's the Exact Value for Sin 13π/12 degrees ? Without using a calculator
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #370420 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
\"13pi%2F12=pi%2Bpi%2F12\" , so our reference angle is \"pi%2F12\"
\n" ); document.write( "We calculate by reference to angles in the first quadrant whose terminal sides are reflections on the axes or the origin, and whose trigonometric functions have the same absolute value.
\n" ); document.write( "The two angles differ by \"pi\" or \"180%5Eo\"
\n" ); document.write( "\"pi%2F12\" is in the first quadrant, where sine and cosine are positive, while
\n" ); document.write( "\"13pi%2F12\" is in the third quadrant where sine and cosine are negative.
\n" ); document.write( "\"sin%2813pi%2F12%29=-sin%28pi%2F12%29\"
\n" ); document.write( "The only angles in the first quadrant whose trigonometric function values I remember are \"0\", \"pi%2F6\", \"pi%2F4\", \"pi%2F3\" and \"pi%2F2\" (0, 30, 45, 60, and 90 degrees).
\n" ); document.write( "For any other angles, I need those trigonometric identity formulas.
\n" ); document.write( "I search for them, and find
\n" ); document.write( "\"sin%28alpha%2F2%29=sqrt%28%281-cos%28alpha%29%29%2F2%29\" with a sign to be determined
\n" ); document.write( "I know that \"cos%28pi%2F6%29=sqrt%283%29%2F2\"
\n" ); document.write( "\"pi%2F12=%28pi%2F6%29%2F2\", and both angles are in the first quadrant with positive values for ther trigonometric functions, so
\n" ); document.write( "
\n" ); document.write( "(If there is a way to make it look prettier than that, I do not know it.)
\n" ); document.write( "So \"highlight%28sin%2813pi%2F12%29=-sqrt%282-sqrt%283%29%29%2F2%29\"
\n" ); document.write( "
\n" );