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How do you find the exact value of #arctan [tan (-(2pi)/3)]#?

Answer 1

#-(2pi)/3#

It is defined that #f^-1(f(x))=x#, or when you plug a value into a function, and then plug the outputted value into the inverse function, you will get the value you started with.

Read the intro for more info about inverse functions

Since #arctan(x)# is identical to #tan^-1(x)#, we can use the above property of mathematics to say that #tan^-1(tan(-(2pi)/3)) = -(2pi)/3#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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