arctan

9.3

An angle whose tangent equals a given number

noun
/ˈɑrkˌtæn/

Specialized

: arcotangente

Theta, right, You're right, it's arctan sine Theta over Cos Theta, which is Theta, right?

Examples

So I'm going to get minus arctan of one.
And if you think about the graph of arctan, it looks like this.
Of course we're left with arctan of Four Thirds X.
And let's look at arctan TDT.
So I'm going to use arctan in this case just for familiarity.
I generated the curve by plotting arctan() in Excel and stripping out all the usual chart stuff.

Blog text (11)
When calculating angles in trigonometry, the arctan function helps find the angle whose tangent is a specific value.
In mathematics, arctan is used to determine the angle from a given tangent ratio, commonly represented as arctan(y/x).
To find the angle for a slope, you would apply the arctan of the rise over the run in a right triangle.

Synonyms

arc tangent

vsarctan

Specialized

1 7.9

The angle whose tangent equals a given number

is written as two words instead of a single form

inverse tangent

vsarctan

Specialized

1 6.5

A math function that gives the angle whose tangent equals a number

is a more technical descriptive phrase rather than a literal symbol

arctangent

vsarctan

Specialized

9.9

The angle whose tangent is a given number

is written as a short symbolic name rather than the full word

Surface Forms

arctan singular

arctans plural

Morphology

arctan = arc + tan (semi-transparent) = arc + tan

Composition of 'arc' + 'tan' is clear, but the technical meaning 'inverse tangent' requires specific mathematical knowledge and is not obvious to general learners.

Etymology

The word arctan is a short form of arc and tangent. Tangent comes from a Latin word meaning 'to touch', and arc means an 'angle' or curve, so arctan gives the angle when you know the tangent, the 'touch' ratio.