SOLUTION: Use a sum or difference formula to find the exact value of cot 11pie/12

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
..
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.
..
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
RELATED QUESTIONS
Use a sum or difference formula to determine the value of the trigonometric function.... (answered by lwsshak3)

Use a sum or difference formula to determine the value of the trigonomic function... (answered by lwsshak3)

Find the exact value of sin(7pi/12) by using a sum or difference formula. (answered by Edwin McCravy)

Use the angle sum or difference identity to find the exact value of cos195... (answered by Edwin McCravy)

find exact value of cos pi/12 by using a sum or difference formula (answered by Shin123,Alan3354)

Use a sum or difference formula to find the exact value of the following.... (answered by lwsshak3)

Use a sum or difference formula to find the exact value of the following. cos 7pi/10... (answered by lwsshak3)

Use a sum or difference formula to find the exact value of the following: {{{... (answered by lwsshak3)

Use a sum or difference formula to find the exact value of the following. {{{... (answered by ikleyn)