What is the domain of y = tan x?

Question

anonymous · Answer

attachment

anonymous · Answer

@mathmale  A?

anonymous · Answer

@amistre64

mathmale · Answer

Remember, Spikers, that the cot x function is periodic.  It repeats itself indefinitely.  Pi is the period of just ONE cycle of the cot x function.

If y ou were to draw y=cot x, you'd have the first cycle, of length Pi, beginning at x=0.  But there'd be repetitions of the same graph on the right and on the left.   So, using this info, judge which of the given answers is best.  It's not Pi, by the way.

michele_laino · Answer

hint:
since we have the subsequent definition:
$$\tan x = \frac{{\sin x}}{{\cos x}}$$
then tangent function is not defined at point such that: $\cos x=0$

michele_laino · Answer

points*

retireed · Answer

y is not defined for pi/2 or (3 pi) / 2 for 0 <= X <= 2 pi

anonymous · Answer

b.

michele_laino · Answer

b is a wrong option, since $\cos 0=1$ and $ \cos \pi=-1$

mathmale · Answer

I know this is taking a lot of time, but still strongly recommend that you graph one cycle of y=cot x before trying to proceed further.

michele_laino · Answer

namely tangent function exists inside $(0,1)$ except one point

mathmale · Answer

sorry, very sorry.  It's y=tan x we're discussing.  Everyone in agreement?

michele_laino · Answer

oops.. I meant $(0, \pi)$

mathmale · Answer

Michele, the basic, central graph of the tangent function has the domain (-pi/2 , +pi/2), not (0, pi) (unless you're talking about the cot x function.

zarkon · Answer

Michele_Laino  is clearly talking about the guess the original poster made   $(0,\pi$)

mathmale · Answer

But we need to find the domain  for multiple cycles of the tangent function.  Thus, b is incorrect because that's the domain of ONLY ONE CYCLE of the cot. function.

michele_laino · Answer

no, please it is my explanation in order to say that option b is a wrong option @mathmale

mathmale · Answer

Point made, point correct, point taken, apologies issued.  :)

mathmale · Answer

So, we eliminate answer choices a and b.  Of the remaining two choices, which is correct, and why?

mathmale · Answer

Spikers, your input, please!

zarkon · Answer

I think Spikers is waiting for someone to give the answer

mathmale · Answer

I do notice that Spikers has typed in a message here ONLY ONCE, and that was to  state that the answer is "b" without explanation.  Spikers?  Time for further input from you.

mathmale · Answer

Spikers, if I were  you I'd do a search for "y=tan x" and look carefully at the graphs that pop up.  You should eventually be able to determine the domain of a function simply by looking at the graph.  That certainly works for y=tan x, if not for every other function.

mathmale · Answer

sorry, I have to get off the 'Net.