document.write( "Question 1201900: Evaluate:\r
\n" ); document.write( "\n" ); document.write( "arccos[cos(-4pi/3)] \n" ); document.write( "

Algebra.Com's Answer #836466 by ikleyn(52834) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Evaluate: $\"arccos%28cos%28-4pi%2F3%29%29\"$
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The angle    lies in the second quadrant, QII.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The cosine function of this angle has a negative value.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "They want you find  the angle,  ,  which has the same value of cosine as the angle  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "arccos is, BY THE DEFINITION,  an angle in the range from 0 to ,  [0,).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, they want you find an angle in the range  [0,),  which has the same cosine value,\r\n" );
document.write( "as  .  It is the angle in the range  [0,),  which has the same projection on x-axis\r\n" );
document.write( "as the angle  .  The desired angle is,  ,   .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Geometrically, it is the same angle as  ,  but this    is expressed and presented in the right range.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This  EXACT  value is  PRECISELY  what they want from you.  There is  NO  NEED  to transform it to numerical value in radians.\r\n" );
document.write( "You may transform it in radians for the sake of your curiosity, if you want, but in reality, it is  NOT  NEEDED.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "This exact value,  ,  is  PRECISELY  what they want from you.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.   = .\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved, with all necessary explanations.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "In solution of this problem, the major step is to get a precise understanding
\n" ); document.write( "what they want from you, and formulate it clearly, as I did it in my post.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To understand my solution better, read and re-read it several times: as many times,
\n" ); document.write( "as you need to get FULL UNDERSTANDING.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I know that for beginner students, such problems are difficult and perplex them.\r
\n" ); document.write( "\n" ); document.write( "The only way to crawl into this area is to get it from an expert and read and re-read it as many times,
\n" ); document.write( "as it is needed for full understanding. There is NO OTHER WAY.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "/////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If you want to see other similar and different solved problems, look into the lesson\r
\n" ); document.write( "\n" ); document.write( " - Advanced problems on calculating trigonometric functions of angles\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );