Posted by Chris on Monday, May 18, 2009 at 8:34pm.
I do not understand for my life how to solve this problem.
Evaluate the expression without the aid of a calculator.
arccos[(3^1/2)/2)
I'm not sure how my teacher did it. I know she said to find which quadrant that cos can be in and graph the triangle to find the angle.

trig  Reiny, Monday, May 18, 2009 at 9:11pm
first of all
3^(1/2) = √3
arccos[(3^1/2)/2) really says :
find the angle theta, so that
cos theta = √3/2
are you familiar with the ratio of sides of the 306090 triangle ?
if so, then you should recognize that cos 30º = √3/2
but our cosine is negative so the angle must be in quadrants II or III by the CAST rule. (and 30º = pi/6 radians)
so theta is pi  pi/6 = 5pi/6
or
theta is pi + pi/6 = 7pi/6
then arccos[(3^1/2)/2) = 5pi/6 or 7pi/6