What causes alternating patterns in the graph of tan(x)/cos(x)?

  • Thread starter AdrianHudson
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In summary, the conversation discusses a graph of tan(x) and tan(x)/cos(x) on the same axis. It is noted that when cos(x) is greater than 0, tan(x)/cos(x) resembles tan(x), and when cos(x) is less than 0, it resembles -tan(x). This creates an alternating pattern on the graph. The speaker is seeking an explanation for this phenomenon.
  • #1
AdrianHudson
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I just recently discovered for myself this weird graph, can anyone explain to me what is exactly happening here. I realize there are a couple asymptotes but I am confused on when when y<0 the "legs" of the graph converge on another asymptote it looks like the tan(x) is just repeated but flipped so it goes:
Normal tan(x) look then the second one will be tan(x) with a flip on the y-axis then it goes back to the normal tan(x) graph. Weird. Care to explain what's happens?

P.S sorry about if this is in the wrong section :)
 
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  • #2
Sorry about little typos I'm on my phone.
 
  • #3
Plot tan(x) and tan(x)/cos(x) on the same axis
http://www.wolframalpha.com/input/?i=plot+{tan(x)/cos(x),tan(x)}

What is happening is
when cos(x)>0 to tan(x)/cos(x) looks a lot like tan(x)
when cos(x)<0 to tan(x)/cos(x) looks a lot like -tan(x)
So those two are alternating.
 

FAQ: What causes alternating patterns in the graph of tan(x)/cos(x)?

What is the domain of the graph of tan(x)/cos(x)?

The domain of the graph of tan(x)/cos(x) is all real numbers except for the values of x where cos(x) is equal to 0. This means that the graph has vertical asymptotes at x = π/2, 3π/2, 5π/2, etc.

What is the range of the graph of tan(x)/cos(x)?

The range of the graph of tan(x)/cos(x) is all real numbers. This is because tan(x) and cos(x) can take on any value, so their quotient can also take on any value.

How many x-intercepts does the graph of tan(x)/cos(x) have?

The graph of tan(x)/cos(x) has infinitely many x-intercepts, as it crosses the x-axis every time cos(x) equals 0. This happens at x = π/2, 3π/2, 5π/2, etc.

What are the asymptotes of the graph of tan(x)/cos(x)?

The graph of tan(x)/cos(x) has vertical asymptotes at x = π/2, 3π/2, 5π/2, etc. These are the values of x where cos(x) equals 0 and the graph approaches infinity.

How does the graph of tan(x)/cos(x) compare to the graph of tan(x)?

The graph of tan(x)/cos(x) is similar to the graph of tan(x), but it is shifted to the left by π/2. This is because the denominator, cos(x), has a period of 2π, while the numerator, tan(x), has a period of π. This results in a horizontal shift of π/2.

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