Question 828431
find the exact value of cot (13π/3)and show the steps 
{{{cot(13pi/3)=1/tan(13pi/3)}}}
tan half-angle formula: {{{tan(s/2)=sin(s)/(1+cos(s))}}}
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{{{tan(13pi/3)=tan(26pi/3)/2=sin(26pi/3)/(1+cos(26pi/3))}}}
26&#960;/3=2&#960;/3 or reference angle of &#960;/3 in quadrant II in which sin>0, cos<0.
sin(26&#960;/3)=sin(&#960;/3)=&#8730;3/2
cos(26&#960;/3)=cos(&#960;/3)=-1/2
tan(13&#960;/3)=(&#8730;3/2)/(1-1/2)=&#8730;3
cot(13&#960;/3)=1/tan(13&#960;/3=1/&#8730;3=&#8730;3/3
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calculator check:
tan(13&#960;/3)&#8776;1.7320..
Exact value=&#8730;3&#8776;1.7320..