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How do you evaluate #arctan(sqrt(3))#?

Answer 1

Nolan Alexander

Evaluate #arctan (sqrt3)#

#tan x = sqrt3#. Trig table gives --># arc x = pi/3# or 60 deg

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Answer 2

Charles Autterson

To evaluate ( \arctan(\sqrt{3}) ):

Using the properties of the tangent function, we know that: [ \tan\left(\frac{\pi}{3}\right) = \sqrt{3} ]

Thus, [ \arctan(\sqrt{3}) = \arctan\left(\tan\left(\frac{\pi}{3}\right)\right) ]

Using the inverse property of the tangent function: [ \arctan(\tan(x)) = x ]

Substituting ( \frac{\pi}{3} ) for ( x ): [ \arctan(\sqrt{3}) = \frac{\pi}{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.