SOLUTION: find the exact value of cot (13π/3)and show the steps

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Question 828431: find the exact value of cot (13π/3)and show the steps
Answer by lwsshak3(11628) About Me  (Show Source):
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find the exact value of cot (13π/3)and show the steps
cot%2813pi%2F3%29=1%2Ftan%2813pi%2F3%29
tan half-angle formula: tan%28s%2F2%29=sin%28s%29%2F%281%2Bcos%28s%29%29
..
tan%2813pi%2F3%29=tan%2826pi%2F3%29%2F2=sin%2826pi%2F3%29%2F%281%2Bcos%2826pi%2F3%29%29
26π/3=2π/3 or reference angle of π/3 in quadrant II in which sin>0, cos<0.
sin(26π/3)=sin(π/3)=√3/2
cos(26π/3)=cos(π/3)=-1/2
tan(13π/3)=(√3/2)/(1-1/2)=√3
cot(13π/3)=1/tan(13π/3=1/√3=√3/3
..
calculator check:
tan(13π/3)≈1.7320..
Exact value=√3≈1.7320..