# Bit foggy on this trig question

1. Dec 2, 2008

### yoleven

1. The problem statement, all variables and given/known data
arccos(cos2$$\Pi$$)

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

2. Dec 2, 2008

### 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).

3. Dec 2, 2008

### 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

4. Dec 2, 2008

### 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

Last edited: Dec 2, 2008
5. Dec 4, 2008

### HallsofIvy

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