Question 969303
cos theta = 2/3 and theta is acute find cot theta
<pre>
Here are the steps to follow:

Draw a right triangle. Label an angle <font face="symbol">q</font>:

{{{drawing(200,230,-.5,2.5,-.5,sqrt(5)+.5,triangle(0,0,2,0,2,sqrt(5)),
locate(.3,.3,theta)


)}}}


Since {{{matrix(1,3,cosine,""="",adjacent/hypotenuse)}}}, label the
side adjacent to <font face="symbol">q</font> as the numerator of {{{2/3}}}, which is 2, and
label the hypotenuse as the denominator of {{{2/3}}}, which is 3.

{{{drawing(200,230,-.5,2.5,-.5,sqrt(5)+.5,triangle(0,0,2,0,2,sqrt(5)),
locate(1,0,2),locate(1,1.5,3),locate(.3,.3,theta)


)}}}


Use the Pythagorean theorem to find the third side which is the
side opposite to <font face="symbol">q</font>. Label the side opposite to <font face="symbol">q</font> as what you get. 
(It will be a square root.)

Then use the fact that {{{matrix(1,3,cotangent,""="",adjacent/opposite)}}} to get the answer.  
Be sure to rationalize the denominator.

Edwin</pre>