Trig graph problem

1. Sep 22, 2005

özge

i have a trigonometry question and i really dont know how to solve i checked couple of books but still no hope here it is:

im supposed to draw the graph of y=cos¶/3(x-1) but i couldnt

2. Sep 22, 2005

Tom Mattson

Staff Emeritus
Your equation is showing up funny on my browser.

Is it supposed to be this:

$$y=cos(3x-1)$$

or this:

$$y=cos(\frac{1}{3x-1})$$

?

3. Sep 22, 2005

arildno

y=cos¶/3(x-1)???????????????????????????????????????????????????
Neither can I. Please type in the CORRECT formula.

4. Sep 22, 2005

Lisa!

I think it's something else!

5. Sep 22, 2005

özge

y=cos pi/3(x-1)

now ok?

6. Sep 22, 2005

arildno

Ok, so it is:
$$y=\cos(\frac{\pi}{3x-1})$$

Hints:
1. Find the point of singularity, where y is not defined.
2. Determine the set of points were y is -1, 0, 1 respectively.
In particular, see what this implies for the function's behaviour very close to the singularity found in 1.

7. Sep 22, 2005

özge

ok it is not that y is equal to cos multiplied by pi/3 multiplied by (x-1)

8. Sep 22, 2005

Tom Mattson

Staff Emeritus
Still not OK, and I suspect that it's because you aren't placing your parentheses properly.

What you have written is this:

$$y=cos(\frac{\pi}{3x-1})$$.

Now that's a perfectly legitimate function, but I strongly suspect that it is not the one you are supposed to graph, simply because it's too difficult for a trigonometry course. I am inclined to think that you really meant this:

$$y=cos[\frac{\pi}{3}(x-1)]$$.

Am I right?

9. Sep 22, 2005

özge

(x-1) isnt near 3

10. Sep 22, 2005

Tom Mattson

Staff Emeritus
I don't know what that means.

11. Sep 22, 2005

arildno

özge:
If Tom Mattson is right, here's how you could have written this properly:
y=cos(pi*(x-1)/3)

12. Sep 22, 2005

özge

u are right

13. Sep 22, 2005

Tom Mattson

Staff Emeritus
This can't be right. cos without an argument makes no sense.

14. Sep 22, 2005

arildno

Do you know what the cosine function is??
What is its argument?

15. Sep 22, 2005

özge

what u wrote :$$y=cos[\frac{\pi}{3}(x-1)]$$
was right im sorry im new to these things and i diddnt know how to write

16. Sep 22, 2005

Tom Mattson

Staff Emeritus
Alrighty then!

Here are a couple of tips to get you started.

*Examine the graph of $y=cos(x)$.

*Note that if you have the graph of some function $y=f(x)$ then you can obtain the graph of $y=f(x+a)$ by shifting the graph of $y=f(x)$ horizontally by $a$ units. You move to the right if $a<0$ and to the left if $a>0$.

*The period $T$ of a cosine function $y=A\cos[k(x+a)]$ is $T=\frac{2\pi}{k}$.

Give it a shot and see how you do, OK?

17. Sep 22, 2005

ok, thanks