# Trig problem--equation for asymptote (sp?) **URL:** \ **Category:** Factual Questions\ **Created:** [September 9, 2002, 7:56pm UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697 "2002-09-09T19:56:27Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![MovieMogul](https://avatars.discourse-cdn.com/v4/letter/m/f08c70/32.png) [@MovieMogul](https://boards.straightdope.com/u/MovieMogul)\ **Post date:** [September 9, 2002, 7:56pm UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/1 "2002-09-09T19:56:27Z")
It has been years since I have taken any math, but I have come across a problem in my job where I need to chart a line that (as currently plotted) is asymptotic to the X-axis and arcs up. How do I derive an equation for this line? The data points fall in a fairly good pattern but don’t line up exactly. If I was plotting a straight line, I know how I’d do it, but I don’t remember how to with a curve. Any help would be appreciated (and if I’ve left something critical out, let me know). Thanks! ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [September 9, 2002, 9:54pm UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/2 "2002-09-09T21:54:15Z")
You mean it’s asymptotic with the x-axis to the left, but as it goes right (positive), it arcs up? This would be the exponential function, y=k_e^(a_x). If you take the logarithm of the y-values before you plot it, you can then fit a straight line through it. If the curve you’re talking about is asymptotic to the right, and goes up as it approaches zero (IOW, also asymptotic to the y-axis), that is the y=1/x curve, you can fit a straight line by taking one over the y-values first. ---
**Author:** ![g8rguy](https://avatars.discourse-cdn.com/v4/letter/g/7cd45c/32.png) [@g8rguy](https://boards.straightdope.com/u/g8rguy)\ **Post date:** [September 9, 2002, 11:24pm UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/3 "2002-09-09T23:24:53Z")
Okay, first try plotting ln(y) vs x; if y = exp(A_x+B), then ln(y) vs x will give you a straight line (ln(y) = A_X+B). Also try plotting ln(y) vs ln(x), if y = A_x[sup]n[/sup] then ln(y) vs ln(x) will give you a straight line instead (ln(y) = ln(A) + n_ln(x)). If it’s diverging near the x axis, the latter is probably the one you want. It is, of course, entirely possible that it’s neither a simple exponential nor a simple power, in which case things just got a whole lot harder. ---
**Author:** ![JS\_Princeton](https://avatars.discourse-cdn.com/v4/letter/j/57b2e6/32.png) [@JS\_Princeton](https://boards.straightdope.com/u/JS_Princeton)\ **Post date:** [September 9, 2002, 11:32pm UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/4 "2002-09-09T23:32:01Z")
Alternatively you can use the negative arctangent function shifted up by pi/2. ---
**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\ **Post date:** [September 10, 2002, 4:49am UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/5 "2002-09-10T04:49:52Z")
You could try using the [Least Squares Method](http://www.efunda.com/math/leastsquares/leastsquares.cfm). ---
**Author:** ![sailor](https://avatars.discourse-cdn.com/v4/letter/s/a587f6/32.png) [@sailor](https://boards.straightdope.com/u/sailor)\ **Post date:** [September 10, 2002, 6:52am UTC](https://boards.straightdope.com/t/trig-problem-equation-for-asymptote-sp/127697/6 "2002-09-10T06:52:01Z")
There are an infinite number of curve equations so there is no one simple answer. If the curve follows some law then you might find a specific function (exponential, log, whatever) which represents the curve but as a general rule for finding a function you would be looking for polinomials and even then there are many ways of going about it. Personally I have used Chebyshev’s polinomials in the past but there are many others you can use.