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Calculate cot−1

x= adjacent_side/opposite_side




cot−1(x)

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

Formula

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

θ = cot−1(Length_of_Adjacent_side / Length_of_Opposite_side)

Calculate Cot Inverse

The inverse cotangent (cot-1 or arccot) of a value is the angle whose cotangent is the given value. It is used to find angles when the cotangent value is known.

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

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

where:

Example 1

Let's calculate the inverse cotangent of 1:

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

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

Example 2

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

The angle whose cotangent is \( \sqrt{3} \) is 30 degrees or \( \frac{\pi}{6} \) radians. So:

\( \cot^{-1}(\sqrt{3}) = 30^{\circ} = \frac{\pi}{6} \)

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