SOLUTION: Use a sum or difference formula to determine the value of the trigonometric function. cot(-7pi/12)
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Question 589049: Use a sum or difference formula to determine the value of the trigonometric function. cot(-7pi/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 trigonometric function. cot(-7pi/12)
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Use the more familiar tan addition formula:
cot(-7π/12)=1/tan(-7π/12)
tan(-7π/12)=tan(2π/12-9π/12)=tan(π/6-3π/4)
tan addition formula:
tan(s-t)=(tan s-tan t)/(1+tan s tan t)
..
tan(π/6-3π/4)=(tan π/6-tan 3π/4)/(1+tan π/6)*tan 3π/4)
tan π/6=√3/3
tan 3π/4=-1 (quadrant II where tan<0)
tan(π/6-3π/4)=(√3/3+1)/(1+√3/3*-1)
tan(-7π/12)=(1+√3/3)/(1-√3/3)≈3.732
cot(-7π/12)=(1-√3/3)/(1+√3/3)≈.268
Check with calculator:
tan(-7π/12)≈3.732
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