Sketching y = x arccos(x)

**The question:**

Sketch the following curve, showing its main features:

$\displaystyle y = xcos^{-1}(x)$

I'm not sure how to attempt this. I know that the inverse of cosine is restricted to [-1, 1] in the domain, and must be restricted on the range to allow it to have an inverse, i.e. $\displaystyle [0, \frac{\pi}{2}]$ I know the graph passes through the origin too. I'm stumped in regards to sketching it. I don't think I have all the information. Any assistance would be great!