Represent inverse trig function as another inverse trig function

Question

I'm struggling with this one. How can I respesent some inverse function as another inverse function? Is it possible to represent let's say $\arctan(-2)$ in terms of $\arccos(…)$, $\arcsin(…)$, $\text{arccot(…)}$?

Specific examples:

$\arctan{(-2)}$ respresented as $\arccos$

$\arcsin{(-\frac{3}{4}})$ respresented as $\arctan$

$\arctan{(-3)}$ represented as $\arcsin$

I suppose it has to do something with the right triangle, and this is the part that I'm struggling with. I do know how to apply trigonometric functions to the right triangle thing, but no idea how to do it with inverse ones.

Thank you!

Answer 1

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