Very basic precal question about cotangent and tangent

[Ghost803]

So, I just learned in class that to get inverse cot^-1(x) I have to do tan-¹(1/x). Then add either pi, or 180 depending on wheather we are using radians or degrees.

And I don't understand this. If x is cot, then when we do 1/x, shouldn't we get tan? And after than isn't it enough to just do tan^-1(1/x) to get the answer? What is the point of adding that pi or 180 degrees?

 

[tiny-tim]

So, I just learned in class that to get inverse cot^-1(x) I have to do tan-¹(1/x). Then add either pi, or 180 depending on wheather we are using radians or degrees.

And I don't understand this. If x is cot, then when we do 1/x, shouldn't we get tan? And after than isn't it enough to just do tan^-1(1/x) to get the answer? What is the point of adding that pi or 180 degrees?

Hi Ghost803!

That only applies to negative values of x.

It all depends on the definition of principal value.

For tan, the principal value is between ± π/2 (because tan = ±∞ at ±π/2)

but for cot, the principal value is between 0 and π (because cot = ±∞ at 0 and π).

(see http://en.wikipedia.org/wiki/Inverse_trigonometric_functions)

So for cot^-1(x) for negative x, tan^-1(1/x) would be < 0, which is not a principal value for cot, so you have to add π