# How do you graph a Tangent/cot function?

1. Dec 12, 2006

### AznBoi

How do you graph a Tangent/cot function??

Does anyone know a site where I could find information on PreCal curriculum? Does anyone mind explaining to me how to graph a Tan/cot function? I get all the other trig function graphs, just not this one. How do you find the period? I'm confused about where to put the asymptotes when you have a "b" change in the number that is in front of "x". Thanks a lot!

2. Dec 12, 2006

### AznBoi

Now I know how to find the asymptotes. Is the period of tan/cot always pi??

3. Dec 12, 2006

### cristo

Staff Emeritus
Well, the period of tan(x) is always pi! But, like other trigonometric functions, changing the function to, say, tan(ax) will alter the period. For example, consider the sine function. sin(2x) has a period of half the period of sin(x).

Here is link to a page with an interactive version of the graph of tan (click on interactive tutorial) It allows you to change the "number in front of x" and observe the changes to the graph.

http://www.analyzemath.com/Tangent/Tangent.html

4. Dec 12, 2006

### d_leet

What is tan(x)/cot(x) in terms of sines and cosines? What is this also equal to?

5. Dec 12, 2006

### cristo

Staff Emeritus
I don't think he means tan(x)/cos(x), he means tanx or cosx. However, using a slash to mean "or" in a situation which could be mistaken as a mathematical formula, is rather clumsy!

6. Dec 12, 2006

### AznBoi

Ok, thanks. I got it all figured out. So the period would of tan and cot graphs would be pi/b having "b" be the number before "x" in the function. right??

Ok, I came up with this formula to find the vertical asymptotes. Can someone please verify these formulas?

When y=a tan (bx-c)

For Tan asymptotes: bx-c=pi/2 and bx-c=-pi/2

For Cot asymptotes: bx-c=0 and bx-c=pi

Thanks a bunch!