document.write( "Question 1202696: If tan x > 0, then tan (x/2) > 0. True or False? \n" ); document.write( "

Algebra.Com's Answer #837770 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "\r\n" );
document.write( "This problem is remarkable.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It is remarkable, because one single example (or \"counter-example\") is enough to disprove the statement.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "And even if a student does not have a calculator, he (or she) must know \r\n" );
document.write( "the table values of trigonometric functions.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    In particular,  tan(240°) =   (in 3rd quadrant), \r\n" );
document.write( "\r\n" );
document.write( "    while tan(240°/2) = tan(120°) =   (in 2nd quadrant).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This single fact disproves the statement.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  False.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Good problem to learn (may be, for the first time), how counter-examples work in Math.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );