Question 960601
cos theta = 7/25 and theta is not acute, find the value of tan 1/2 theta
<pre>
{{{tan(expr(1/2)theta)}}}{{{""=""}}}{{{(1-cos(theta))/sin(theta)}}} 

So we will need {{{sin(theta)}}}.  So we will need the identity:

{{{sin(theta)= "" +- sqrt(1-cos^2(theta))}}}

Since <font face="symbol">q</font> is not acute, it is not in the 1st quadrant and the only other quadrant
that the cosine is positive in is the 4th quadrant.  The sine is negative in
the 4th quadrant, so the identity uses the - sign:

{{{sin(theta)= -sqrt(1-cos^2(theta))}}}{{{""=""}}}{{{-sqrt(1-(7/25)^2)}}}{{{""=""}}}{{{-sqrt(1-49/625)}}}{{{""=""}}}{{{-sqrt(625/625-49/625)}}}{{{""=""}}}{{{-sqrt(576/625)}}}{{{""=""}}}{{{-24/25}}}  

{{{tan(expr(1/2)theta)}}}{{{""=""}}}{{{(1-cos(theta))/sin(theta)}}}{{{""=""}}}{{{(1-(7/25))/(-24/25)}}}

Multiply top and bottom by 25

{{{tan(expr(1/2)theta)}}}{{{""=""}}}{{{(25-7)/(-24)}}}{{{""=""}}}{{{-18/24}}}{{{""=""}}}{{{-3/4}}}

Edwin</pre>