c3 inverse trig functions

For inverse trig functions, say if I want the $cos^{-1}(\frac{-\sqrt{3}}{2})$, as it's inverse cos, I know the domain has to be $0<x<\pi$ so because the value isn't within this range...

Perhaps you are confusing range and domain?

If $f(x) = \arccos(x)$

then

the domain is $-1\le x \le 1$

and

the range is $0\le f(x)\le \pi$

Thanks, yes I was. So as it's within the correct range, can I just put it through the calculator?

Yes.

Yes.

So, in general, I should use the relevant graph to find the correct value in the appropriate domain. Once I've obtained that, I can just put it through my calculator (unless it's a value that I know whereby the calculator isn't needed)?

I basically hate the unit circle so the above will always be ok?

Could you give an example of the type of problem that you're trying to solve?

Considering a relevant graph is often a good idea.

remember that

Cos( 90 - x )° or

Cos( π/2 - x )

are both equivalent to Sin x.

thus Sin (4π/3) is the same as Cos( π/2 - 4π/3 )

and also Cos( -β ) is the same as Cos( β )

thanks bear