Inverse trigonometric function: Arctangent (arctg)
Content

Definition

Arctangent (arctg or arctan) is the inverse trigonometric function.

Arctangent x defined as the inverse function of the tangent xWhere x – any number (x∈ℝ).

If the tangent of the angle у is х (tg y = x), which means arc tangent x equals y:

arctg x = tg-1 x = y, and -π/2y<π/2

Note: tg-1x means inverse tangent, not tangent to the power -1.

For example:

arctg 1 = tg-1 1 = 45° = π/4 rad

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The arctangent function is written as y = arctg (x). The chart in general looks like this:

Inverse trigonometric function: Arctangent (arctg)

Arc tangent properties

Below in tabular form are the main properties of the arc tangent with formulas.


арктангенса»>Тангенс

арктангенса


арктангенсов»>Разность

арктангенсов

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


арктангенса»>Синус

арктангенса

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


арктангенса»>Косинус

арктангенса

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


дроби»>Арктангенс

дроби

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


из арксинуса»>Арктангенс

из арксинуса

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


арктангенса»>Производная

арктангенса

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)


интеграл арктангенса»>Неопределенный

интеграл арктангенса

» data-order=»Inverse trigonometric function: Arctangent (arctg)«>Inverse trigonometric function: Arctangent (arctg)Inverse trigonometric function: Arctangent (arctg)

PropertyFormula
«>Inverse trigonometric function: Arctangent (arctg)
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Arctangent table

-90 °-p/2-∞
-71.565 °-1.2490-3
-63.435 °-1.1071-2
-60 °-p/3-45 °-p/4-1
-30 °-p/6-26.565 °-0.4636-0.5
00
26.565°0.46360.5
30°Π / 645°Π / 41
60°Π / 363.435°1.10712
71.565°1.24903
90°Π / 2
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