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How do you evaluate ##tan(arccos(-3/4))## without a calculator?

Author:
February 20th, 2023

##-sqrt 7/3##
Let ##a = arc cos (-3/4) in Q2##, wherein tangent is also negative.
Then, the given expression is
##tan a = sin a/cos a=-sqrt(1-(-3/4)^2)/(-3/4)=-sqrt 7/3##

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