SOLUTION: Use a sum or difference formula to determine the value of the trigonomic function
cot(-7π/12)
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Question 863196: Use a sum or difference formula to determine the value of the trigonomic function
cot(-7π/12)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Use a sum or difference formula to determine the value of the trigonomic function
cot(-7π/12)
***
cos(-7π/12)=cos(7π/12)=cos(3π/12+4π/12)=cos(π/4+π/3)
Identity: cos(x+y)=cosxcosy-sinxsiny)
cosx=cos(π/4)=√2/2
cosy=cos(π/3)=1/2
sinx=sin(π/4)=√2/2
siny=sin(π/3)=√3/2
cos(x+y)=√2/2*1/2-√2/2*√3/2=√2/4-√6/4=(√2-√6)/4
...
calculator check:
cos(-7π/12)≈-0.2588…
exact value=(√2-√6)/4≈-0.2588…
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