You can put this solution on YOUR website! What would the answer be when you evaluate the function cot(-8pi/3)without a calculator?
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You can think of -8π/3 rotating 2-2/3 π clockwise in a unit circle. This places-8π/3 in quadrant III where a reference angle of π/3 applies and where cot>0
cot(-8pi/3)=1/√3=√3/3