Understanding Arctan: Solving for 0 and 1/0

[hotmail590]

What is arctan(0)?!

I tired using my calculator (its a ti-83 plus) I hit [sec] button then [tan] then [ 0 ] and [ ) ] and it gives me 0 as answer It is in rad mode too (deg mode is same results)

I tried using the google calculator and it gives me 0 also!
http://www.google.com/search?hl=en&q=arctan(0)

BUT my math book says its pie!


Then it tried tan(pi) and indeed that does = 0!

WHY!??!? doenst arctan(0) = pi?



Another question
What is arctan(1/0) ? doens that = impossible?? (if i use my calc it says can't divide by 0)

However the answer is pi/2?!??! WHYYY


Thanks for the help

 

[whozum]

Arctan(x) = Pi means x = tan(pi)

$$tan(\pi) = \frac{0up}{1left} = 0$$

Arctan(x) = 0 means x = tan(0)

$$tan(0) = \frac{0up}{1right} = 0$$

Get it?

2. The answer is in limits.

$$arctan(1/0) = undefined$$

However the limit is defined:

$$\lim x\rightarrow 0 \mbox{ of } arctan(1/x) = \frac{\pi}{2}$$

Try graphing the function arctan(x) and use the trace tool to see the values at those points.

 

[whozum]

Try translating $tan(x) = \frac{sinx}{cosx}$, you might see it more clearly.

 

[Hurkyl]

tan (2pi) = 0 too. So why doesn't arctan(0) = 2pi?

Because there's an important part of the definition of arctan that you're forgetting -- go look at it again.

 

[dextercioby]

HINT:arctan is a function.

Daniel.