Help with finding 1/4 and 3/4 points between consecutive integers of cot and tan

[Johnny_L]

EX Problem:

y =cot(1/4x)

(1)

0 < 1/4x < pi

solve for x, I get: <x< 4pi

So Asymptotes are: (0,4)

(2) Now find 1/4 and 3/4 points between consecutive asymptotes. I know you use A and -A for the y-values, but I m confused as to how you get the x-values. The book says the x-coordinates are negative pi and positive pi.

 

[ksdhart]

Bare with me a moment because this is really confusing me. I'm assuming that you're working with the equation y=cot(x/4), although due to your lack of grouping symbols it could also mean y=cot(1/(4x)). The first part seems okay. From what I can tell you're trying to find two consecutive asymptotes of the function in order to solve part the second part. I believe you simply made a typo at the end where you say the asymptotes are 0 and 4. That should be 0 and 4pi.

Now, the second part is just a confusing mess and I honestly don't even know what you're trying to accomplish. You say "find 1/4 and 3/4 points between consecutive asymptotes?" but what does that mean? Are you needing to find the points that are one-fourth and three-fourths of the way between the two asymptotes? Are you trying to find points where the y-coordinates are 1/4 and 3/4? Something else entirely?

 

[stapel]

y =cot(1/4x)

(1) 0 < 1/4x < pi

Is this interval an answer to something, or part of the question?

solve for x, I get: <x< 4pi

What are you solving? How are you getting an interval (?) for your "solution" value?

So Asymptotes are: (0,4)

How "so"? How to asymptotes relate to the "solving" question?

(2) Now find 1/4 and 3/4 points between consecutive asymptotes.

What do you mean by "1/4 and 3/4 points"? If the asyptotes are the point (0, 4) (which I don't understand either), then how are you defining the new points in relation to this existing point?

I know you use A and -A for the y-values, but I m confused as to how you get the x-values.

What is "A"? What do you mean by the "y-vallues of asymptotes" (which are supposed to be lines of the form "x = (a number)")?

The book says the x-coordinates are negative pi and positive pi.

For what points (not asymptotes) are these numbers the x-coordinates?

When you reply, please include the full and exact text of the exercise, the complete instructions, and a clear listing of your thoughts and efforts so far. Thank you!