Question

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

Answer 1

Please see the explanation.

Explanation:

The inverse tangent function will return a negative angle for this where `cos(theta) = -sin(theta)`. The angle that it returned is:

`theta = -pi/4`

Doing this causes a loss of information, because the condition `cos(theta) = -sin(theta)` occurs in the second AND the fourth quadrant. If you have additional information, regarding which quadrant, you should to one of the two following computations:

For the second quadrant:

`theta = tan^-1(-1) + pi`

`theta = -pi/4 + pi`

`theta = (3pi)/4`

For the fourth quadrant:

`theta = tan^-1(-1) + 2pi`

`theta = -pi/4 + 2pi`

`theta = (7pi)/4`