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Calculate tan−1

x= opposite_side/adjacent_side



Inverse Tangent tan−1() is used to find the angle for a given ratio of the length of the opposite side to the length of the adjacent side, in a right angled triangle.


To find the Inverse Tangent of a given ratio: opposite_side/adjacent_side , use the following formula.

θ = tan−1(Length_of_Opposite_side / Length_of_Adjacent_side)

Calculating Tan Inverse

The inverse tangent (tan-1 or arctan) of a value is the angle whose tangent is the given value. It is used to find angles when the tangent value is known.

The inverse tangent of a value \( y \) is defined as:

\( \tan^{-1}(y) = \theta \)


Example 1

Let's calculate the inverse tangent of 1:

The angle whose tangent is 1 is 45 degrees or \( \frac{\pi}{4} \) radians. So:

\( \tan^{-1}(1) = 45^{\circ} = \frac{\pi}{4} \)

Example 2

Consider another example with the value \( \sqrt{3} \):

The angle whose tangent is \( \sqrt{3} \) is 60 degrees or \( \frac{\pi}{3} \) radians. So:

\( \tan^{-1}(\sqrt{3}) = 60^{\circ} = \frac{\pi}{3} \)

These examples demonstrate how to calculate the inverse tangent of a value.