1. ## Trigonometric Function

The inverse of Cos x is a function. The domain of Cos x could be ???

How would I find the domain???

2. In order for $\displaystyle \textrm{Cos}\,{x}$ to have an inverse function, it must be one-to-one.

Draw the function $\displaystyle \cos{x}$. Can you choose a domain where there aren't any repeating $\displaystyle y$ values?

3. Hmm... I'm assuming that the fact that C is capitalized is significant. I only learned $\displaystyle f(x) = \cos \,x$ when I was in school, and had never seen $\displaystyle f(x) = Cos \,x$ until now. Is it a regional/national thing? I'm in the US.

4. The capitalisation means there has been a standard restriction on the domain of $\displaystyle \cos{x}$. It's up to you to find what that domain is.

Like I said, draw the function, and choose a domain in which there are not any repeating $\displaystyle y$ values.

5. Try looking at this interval.

$\displaystyle [0,\pi]$

edit:// mind blanked.

$\displaystyle [0,\pi]$
Now, can you see WHY they would restrict the domain to be $\displaystyle [0, \pi]$?