Question 205030
 Evaluate 

{{{cos((7pi)/8)}}}


I have this so far 

cos^2 theta=(1/2)(1+cos(2theta))
cos((7pi/8))= sqroot((1+cos(7pi/4))/2)
<pre><font size =4  color = "indigo"><b>       
That step is wrong. You must take the NEGATIVE square root,
not the POSITIVE square root, because {{{7pi/8}}} is in
QII (the second quadrant), and the cosine is negative in
the second quadrant. So you should have had a negative
sign in front of the right side:

    = sqroot((1+ ((sqroot2)/2))/2)
           =sqroot((2+sqroot2)/4)
           
Those are OK except for the sign.  You must recognize
what quadrant you are in whenever you take a square
root, because square roots can be positive or negative.

correct answer:  {{{-(1/2)(sqrt(2+sqrt(2)))}}}  

Edwin</pre>