Question

Find the exact value tan^-1(1)

Answer 1

[AI-generated answer — Bot GPT 3.5]

The value of \( \tan^{-1}(1) \) is equivalent to finding the angle whose tangent is 1.

Since the tangent value is positive, the angle lies in either the first quadrant or the third quadrant.

In the first quadrant, the reference angle \(A\) has a tangent of 1. By constructing a right triangle with opposite side length 1 and adjacent side length 1, we can see that the reference angle is \( \frac{\pi}{4} \) radians or \( 45^\circ \).

In the third quadrant, the corresponding angle \( B \) has a tangent of 1. The reference angle can be found by considering the angle formed by the positive x-axis and the line connecting the origin and a point on the triangle's hypotenuse. This reference angle is \( \frac{\pi}{4} \) radians or \( 45^\circ \).

Therefore, \( \tan^{-1}(1) \) is equal to \( \frac{\pi}{4} \) radians or \( 45^\circ \).