Reciprocal functions and graphs.

[Hutchoo]

Hey!

How do you find the asymptotes/period for a sec(x), cosec(x), cot(x)?
I know it's probably really basic, but I'm getting really confused, meaning I have a gap in my knowledge when it comes to Circular functions.

For example:
Sketch the graph of over the interval of [0, 2]

An obvious asymptote is at 3pi/4, but I'm pretty confused after that.
I'm fine with working out the y-intercepts btw. I'm just confused with the period/asymptote of these functions.

Your help will be a blessing

[monkeywantsabanana]

The asymptotes are simply just the x intercepts of cos(x), sin(x) and tan(x) respectively.

If you were to draw sec(x-pi/4) then draw cos (x-pi/4) then the x intercepts will be the asymptotes and the turning points will be the turning points of sec(x-pi/4) and it'll go in the opposite direction... if that makes sense.

[Hutchoo]

Yep. I understand that. I figured that out just as I posted the thread.
How about something like this:

y = cosec (2x + (pi/3))?
How would you find the asymptotes for that?

[Hutchoo]

OOOOOOOOOOH.
Nevermind, I get it now.