Question 416683: Use a sum or difference formula to find the exact value of cot 11pie/12
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Use a sum or difference formula to find the exact value of cot 11pie/12
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I don't see the cot formula in my book, so I will use the addition formula for tan then take its reciprocal for the cot.
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tan (s+t)=tan(s)+tan(t)/1-tan(s)tan(t)
given 11pi/12 can be divided into 2pi/12 and 9pi/12 or pi/6 and 3pi/4
pi/6 is a 30 degree reference angle(s) in the first quadrant.
3pi/4 is a 45 degree reference angle(t) in the second quadrant.
In the tan addition formula, let s=pi/6 and t=3pi/4
tan(11pi/12)=tan(s+t)=tan(pi/6+3pi/4)=sqrt((3)/3)-1/1-sqrt((3)/3)*(-1)
tan(11pi/12)=sqrt((3)/3)-1/sqrt((3)/3)+1)=.577-1/.577+1=-.423/1.577=-.268
ans:Therefore, cot(11pi/12) is 1/-.268=-3.731
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