Concept

Cotangent

θ

of a right triangle, the cotangent of

θ

is the ratio between the lengths of the adjacent side and the opposite side.

The cotangent of

θ

is written as

cot θ .

$cot θ = \frac{adjacent}{opposite}$

This trigonometric ratio states the ratio between the adjacent side to a certain angle and the opposite side to the angle. It gives no indication about the lengths of the sides.

Right triangle with two vertices movable and the cotangent of one acute angle is computed while the measures change

When the adjacent side and the opposite side lengths for a given angle change, if their ratio stays the same, then the cotangent, too, would stay the same. In addition, note that the cotangent of

θ

is also the reciprocal of the tangent of

θ .

⎩ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎧ cot θ = \frac{adj}{opp} \frac{∣}{∣} tan θ = \frac{opp}{adj} \frac{\frac{∣}{∣}}{∣} \Rightarrow cot θ = \frac{1}{tan θ}

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Concept

Cotangent

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