Excel Tangents for Dummies

tangent to a curve

When it comes to even mildly technical topics, our staffers often find that the contributors to the erstwhile eHow.com were quite happy to mangle terminology they didn't quite comprehend, which more than once led to some serious stupidification of the internet. Liberal arts majors taking on math, even fairly elementary subjects such as middle-school geometry, were responsible for some of the most egregious offenses. Today's example is James T. Wood, whose Techwalla.com article "How to Draw a Tangential Line in Excel" is pretty much par for the course.

For starters, let's define a tangent. According to James,

"A tangential line is a straight line on a graph that runs tangent to a curved line made up of data points."

First, that definition is circular: a tangent is a straight line that touches a curve at a point but does not cross it (locally, anyway). Second, while said curved line is "made up of data points," it is in reality all points that meet the function that's been graphed. James next said,

"Excel has the ability to create a trendline automatically, or you can manually draw the tangential line on the graph."

In the first place, a trendline is not the same thing as a tangent. Second, drawing the tangent manually is very likely not what the OQ had in mind. That manual line? Wood says,

"The tangential line is drawn touching a curved line so that as the curve moves away from the line it is equidistant from the line."

Our staff geometry buff says that's a pretty poor definition of a tangent, mostly because Woods simply reworded his source without quite comprehending it. Without further ado, however, let's see how one actually draws a tangent in Excel¹. The full sequence, with an example, can be found here, but we'll try to summarize it (this method requires that you know the formula of the line).

1. Choose an x value and calculate the y value
2. Choose x values slightly larger and smaller than the target x and calculate the corresponding y values

3. Calculate the secant slope between the target and the new points and interpolate a slope for the target x.
4. Plug the interpolated slope and known x,y into the standard linear equation (y = mx+b) to calculate the corresponding y-intercept.
5. Build a new line using the linear equation and plot it on the same graph

That'll work. James T's method won't work, because he had no idea what he was talking about... just like most of our Dumbass of the Day winners!

¹ Actually, this method approximates a tangent line, but the method uses Excel instead of drawing a trendline (that may have nothing to do with a tangent) and attempting to draw a second line parallel to it.

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