Cotangent formula

About Cotangent formula

One of the six trigonometric functions is cotangent. The term "cot" is commonly used. The cotangent formula, like other trigonometric ratios, is defined as the ratio of the sides of a right-angled triangle. The base and perpendicular ratio of a right-angled triangle is equal to the cot x formula. Here are the abbreviations for six basic trigonometric functions.

Cotangent Formula

Here, c=hypotenuse, a= Opposite side of A, b= Adjacent side of A

For an angle, the cotangent formula is: cot = (adjacent side) / (Opposite side). Consider the right-angled triangle ABC, which is right-angled at B. The side that is adjacent to A is AB, while the side that is opposite to A is BC. Then the cotangent of A (also known as cot A) is,

cot A = (Adjacent side of A) / (Opposite side of A) = (AB) / (BC).

Example, if the value of AB = 3 and BC = 4, then cot A = 3/4.

Properties of Cotangent

We already know that (Adjacent) / cot x (Opposite). Apart from that, there are a number of alternative cotangent ratio formulas in which the cotangent can be expressed in terms of other trigonometric ratios.

Cotangent in Terms of Cos and Sin

(cos θ) / (sin θ) = (Adjacent) / (Hypotenuse) × (Hypotenuse) / (Opposite)

= (Adjacent) / (Opposite)

= cot θ

Thus, cot θ = (cos θ) / (sin θ) is the cot x formula in terms of cos and sin.

Cotangent in Terms of Tan

cot θ = tan (π/2 - θ) (or) tan(90° - θ).

Cotangent in Terms of Cosec

cot θ = √(csc2θ - 1)

Sign of Cotangent

Only the first and third quadrants have a positive cotangent ratio (which includes both tan and cot). In the second and fourth quadrants, it is negative. Thus,

cot (π - θ) = - cot θ (2nd quadrant)

cot (π + θ) = cot θ (3r dquadrant)

cot (2π - θ) = - cot θ (4th quadrant)

cot (2π + θ) = cot θ (1st quadrant)

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