Bit foggy on this trig question

[yoleven]

Homework Statement

arccos(cos2$$\Pi$$)

The Attempt at a Solution

cos of 2$$\Pi$$ =1
how do I get the arccos of 1? Without a calculator.
Thanks

 

[Defennder]

You have to use either some log tables or your memory. More specifically if you know how to sketch the graph of a cos function then you would know immediately that $$\cos (2\pi n) = 1$$ where n is any integer (including 0).

 

[yoleven]

Yes, I know how to get cos of 2$$\Pi$$. It equals 1
I don't know how to get arccos of 1.
Could you help me with that?

I know that, for instance arccos $$\stackrel{\Pi}{4}$$ = $$\stackrel{1}{\sqrt{2}}$$

But how do I figure out arccos 1.

I know it = 0 but I can't see how to derive this

 

[Дьявол]

arccos is inverse function of cos. So If you know that cos(2п)=1 you will know that arccos(1)=2п. Do you understand now?

Regards.

P.S arccos(1 / √2) = п/4

 

[HallsofIvy]

For any number, x, between 0 and $\pi$, arccos(cos(x))= x. That follows from the very definition of "arccos".