# Thread: Sketching y = x arccos(x)

1. ## 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!

2. Originally Posted by Glitch
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!
The domain is [-1, 1]. Yes, (0, 0) is on the curve. I suggest you plot points eg. endpoints (the points where x = 1, -1), 1/2, -1/2 etc. and then try to fit a curve. Are you expected to find turning points? If so, calculus is required.

3. Thanks. The question didn't mention anything about finding turning points. I did that anyway, and it only has one in the interval.

4. Originally Posted by Glitch
Thanks. The question didn't mention anything about finding turning points. I did that anyway, and it only has one in the interval.
plot y &#61; x Arccos&#91;x&#93; - Wolfram|Alpha

5. It's an ugly thing, isn't it? :P

6. Originally Posted by Glitch
It's an ugly thing, isn't it? :P
Everything is relative ....