A helper column is a non-technical term to describe a column added to a set of data to help simplify a complex formula or an operation that would be otherwise difficult. The concept is a little abstract, so here are three examples:

  1. You can use VLOOKUP to perform a lookup with multiple criteria by adding a helper column to the data. In the example above, a helper column is used to concatenate first and last names, so that VLOOKUP can be used to find departments using both names. Click for details on this formula .

  2. You can use a helper column with a formula that returns a value like TRUE for rows that meet specific conditions, then use go to special and delete only those rows. Watch this video to see a “shortcut recipe” to remove specific rows using this technique. The recipe using formulas starts at about 6:00 in the video.

  3. You can use a helper column for sorting. For example, you could add values to a helper column to sort a table in ways not easy or possible with the original set of data. You can also use a helper column to preserve and restore the original sort order.

In Excel, the hyperbolic functions COSH , SINH , and TANH all take a number representing a hyperbolic angle as input. A hyperbolic angle is defined by the area of the sector on the right branch of the unit hyperbola x² - y² = 1, formed by the origin, the point (1,0), and a point on the unit hyperbola. For example, a hyperbolic angle of 1 corresponds to the sector formed on the unit hyperbola with an area of one-half .

The hyperbolic angle of one. - 1

In general, you can think about a hyperbolic angle forming a point on the unit hyperbola, where COSH and SINH give the coordinates of the point:

The point formed by a hyperbolic angle - 2

A negative hyperbolic angle corresponds to a point with a negative y -coordinate.

The point formed by a negative hyperbolic angle - 3

The area of the sector is half the angle’s value to align the hyperbolic functions with their circular counterparts: cosine and sine . This is because the area formed by a circular angle on the unit circle is one-half the angle’s value.

Area of a circular angle. - 4

Dividing by two makes the area of a hyperbolic angle equal to that of a circular angle. For example, the geometry of the hyperbolic and circular functions for the angle a=1 is shown below.

Hyperbolic vs. circular angle. - 5

Unlike a circular angle, whose point rotates periodically around the circle as the angle grows, a hyperbolic angle diverges toward infinity as it increases positively and toward negative infinity as it increases negatively.

As a hyperbolic angle grows larger the corresponding point diverges towards inifinity. - 6

Images courtesy of wumbo.net .