Find the exact real value of arc cos (1/2)

Question

ajprincess · Answer

Let arc cos(1/2)=x
Then cosx=1/2
Can u find x nw?

anonymous · Answer

i think it should be inverse :)

anonymous · Answer

When learning trig, there are several "special" angles one more-or-less memorizes because they are extremely common.  The angle in question is one of them.  If you can't find a reference to these special angles, then use your calculator to do cos inverse and set your angles to degrees or radians, whichever you want.

aravindg · Answer

pi/3

aravindg · Answer

pi/3=3.14/3

anonymous · Answer

Yes, and there actually is an algebraic way of determining the angle, but it is long and involved.  Once one sees it in a trig class, there never is a reason to go back to the derivation because the answer becomes so ingrained that it never becomes necessary to re-create this particular wheel.

anonymous · Answer

|dw:1348933865761:dw|  One would start with this diagram and actually start with the angle FIRST and THEN get the cos, instead of the other way around (the way the question is being asked here).  If anyone wants to see the derivation, I'll go through it.