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

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 $\frac{\pi}{4} r a d$.
So finally we can write that ${\tan}^{-} 1 1 = \frac{\pi}{4}$