Very basic precal question about cotangent and tangent

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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?
 

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tiny-tim
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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! :smile:

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 :wink:
 

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