# Math Help - Inverse cotangent on calculator.

1. ## Inverse cotangent on calculator.

Hello. This should be an easy one, but the answer I'm getting doesn't match the answer in my text book, so I just want someone to help me either confirm it as a misprint or show me what I did wrong:

The question is:

Evaluate the following with a calculator, give the answer in degrees rounded to two decimal places:

$cot^{-1}(-4.2319)$

I get: -13.30 degrees

My text book says: 166.70 degrees

Thanks!

2. for angles in degrees ...

$\cot^{-1}(x) = 90^\circ -\tan^{-1}(x)$

3. On my calculator, I entered: $tan^{-1}(1/-4.2319)$

This works for solving many other problems of this type... can someone explain why this is an exception?

4. For instance, if the problem were:

$csc^{-1}(-3.7893)$

I could enter on my calculator:

$sin^{-1}(1/-3.7893)$

And arrive at the correct answer: -15.30

Why does this apparently work for inverse cosecant but not inverse cotangent?

5. Originally Posted by JennyFlowers
For instance, if the problem were:

$csc^{-1}(-3.7893)$

I could enter on my calculator:

$sin^{-1}(1/-3.7893)$

And arrive at the correct answer: -15.30

Why does this apparently work for inverse cosecant but not inverse cotangent?
the ranges of these two inverses don't match up ...

range of inverse cotangent is from $(0,\pi)$ ... $(0^\circ, 180^\circ)$ , quads I and II

range of inverse tangent is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ ... $(-90^\circ,90^\circ)$ , quads I and IV

6. ## Thank you!

Thanks so much!