Question

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

Answer 1

See explanation.

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`