Trigonometric graphs (1 Viewer)

[Shazer2]

Hello,

I'm just wondering if I can get some assistance sketching some trigonometric graphs. I've been able to do the earlier ones, but when the question changes the period I have trouble. e.g:



So we know the amplitude is 2, so is the period 4pi/2? I am unsure, so if someone can walk me through it, that would be excellent.

Thank you!

 

[Drongoski]

amplitude 2

period = 2 pi/4 = pi/2

 

[Shazer2]

Sorry, I typed the question wrong, it's actually for

 

[Drongoski]

That does not affect the amplitude & period. Question is being kind in requiring you to sketch only for the interval: 0 to pi.

 

[Shazer2]

Alright, well I somehow got the answer. I have another question though, y=tan3x for 0 <= x <= 2pi.

So, the amplitude is 1, and period is pi/3. Now in the answers, they have an asymptote pi/6, but how am I supposed to know that?

 

[Drongoski]

amplitude for tan 3x is not 1. Where, for tanx, asymptotes at x = +- pi/2, now being "more frequent", period is reduced from pi to pi/3, and asymptotes now at +- pi/6 etc etc

 

[Shazer2]

My bad, no amplitude on tan. I still don't understand that

 

[yasminee96]

My bad, no amplitude on tan. I still don't understand that

The asymptotes?
If you really don't understand why - put it in your calculator. Tan inverse (10000000000) = pi/2 (in other words, as tanx approaches infinity, x approaches pi/2)
but you have 3x
so then it'll be pi/2 divided by 3
=pi/6