How do you graph a Tangent/cot function?

In summary, the conversation discusses how to graph a tangent or cotangent function, find its period, and determine the location of asymptotes. It is mentioned that the period of tan(x) is always pi, but can be altered by changing the function to tan(ax). A link to an interactive graph is shared, and the conversation also touches on the relationship between tangent and cotangent functions and their representation in terms of sines and cosines. Finally, a formula is presented for finding the vertical asymptotes of a tangent or cotangent function.
  • #1
AznBoi
471
0
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!
 
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  • #2
Now I know how to find the asymptotes. Is the period of tan/cot always pi??
 
  • #3
AznBoi said:
Now I know how to find the asymptotes. Is the period of tan/cot always pi??

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

What is tan(x)/cot(x) in terms of sines and cosines? What is this also equal to?
 
  • #5
d_leet said:
What is tan(x)/cot(x) in terms of sines and cosines? What is this also equal to?

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
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! :smile:
 

FAQ: How do you graph a Tangent/cot function?

How do you determine the domain and range for a tangent/cot function?

The domain for a tangent/cot function is all real numbers except for values where the function is undefined, which are typically at multiples of π/2. The range for a tangent function is all real numbers, while the range for a cot function is all real numbers except 0.

Can you graph a tangent/cot function without using a calculator?

Yes, you can graph a tangent/cot function by using the unit circle and the properties of the functions. You can also use the values of the tangent/cot function at special angles, such as 0, π/4, and π/3, to plot points on the graph.

How do you find the asymptotes for a tangent/cot function?

The asymptotes for a tangent function occur at odd multiples of π/2, while the asymptotes for a cot function occur at even multiples of π.

What is the relationship between the graphs of tangent and cotangent functions?

The graphs of tangent and cotangent functions are similar in shape, but they are vertically shifted by π/2. This means that when one function is at its maximum or minimum point, the other function is at its asymptote. Additionally, the graphs have a horizontal asymptote at y = 0.

How do you graph a tangent/cot function when it is in a different form, such as a transformed or inverse function?

To graph a transformed tangent/cot function, you can use the same techniques as graphing a basic tangent/cot function, but you will need to apply the transformations to the unit circle values. For an inverse tangent/cot function, you can use the reciprocal property to switch the x and y values on the graph.

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