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How do you find the exact value of #tan^-1 1#?

Answer 1

See explanation.

If you are looking for #tan^-1 1# then you are looking for an acute angle in a triangle where both catheti are equal. Tangent of an angle is a quotient of a cathetus being one of the angle's sides and the opposite one.

The triangle with right angle and 2 equal catheti is an isosceles triangle so its both acute angles are #45^o# or #pi/4rad#.

So finally we can write that #tan^-1 1=pi/4#

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Answer 2

Grace Ashcraft

To find the exact value of arctan(1), you need to identify the angle whose tangent is 1. In this case, the angle is π/4 radians or 45 degrees. Therefore, arctan(1) = π/4 or 45 degrees.

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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.