How to find tan inverse?

Question

in a logarithmic table, in the natural tangents, how do we find tan inverse? like tan^ -1

Answer 1

rather use a calculator!

Answer 2

You mean a table of tangents? You find the tangent value within the body of the table, and then see what angle has that tangent.

e.g. Suppose you want to find the inverse tan of 1.9430. Look through the values in the table of tangents, and the nearest value you can find below it is 1.9375. That's in the 63 degree row, in the 46 column, so it's the tangent of 63 deg 42 min.
You need another 0.0055 to make that up to 1.9430, so look over in the difference column and find 55 (or the nearest to it). It should be in the 4 column, so add that 4 on to the minutes, giving the angle as 63 deg 46 min.

But why would you want to do this? Obviously you have a computer, so even if you haven't a calculator, just call up Excel and type =atan(value) into a cell, or, if you want it in degrees, type in =degrees(atan(1.9430)

Answer 3

The trigonometric tangent is the reciprocal slope of the tangent to the unit circle at that point, ie, the natural tangent (slope) of a line tangent to a circle at 90 degrees is zero (horizontal), but the trigonometric slope at 90 degrees is 1/0 or undefined.

These two results will always be out of phase by 90 degrees. If the table gives a value of X, the trig value will be 90-X.( Watch the algebraic signs.)

Answer 4

Tan takes an perspective as an enter and delivers a ratio as an output. inverse tan ( atan tan^-a million ) takes a ratio as an enter and delivers an perspective as an output. with a view to be sure which to apply you ask your self "am I given an perspective or do I desire to locate an perspective"