Cotangent Formula
Cotangent is one of the six trigonometric ratios which is also denoted as cotan or cot. The cotangent formula is given by the length of the adjacent side divided by the length of the opposite side in a right triangle. There is an interesting relationship between the trigonometric ratios cotangent and tangent which will be seen below.
The relationship of cotangent will also be seen with the trigonometric ratios sin and cos. Let us understand the cotangent formula using the solved examples.
What is Cotangent Formula?
For a given right triangle ABC as shown below, where A is an acute angle,
AB = Hypotenuse
AC = Side adjacent to angle A and between angle A and right angle
BC = Side opposite to angle A
Cotangent Formula is given as follows:
cot A = Adjacent side / Opposite side = AC / BC = b / a
We know that,
tan A = Opposite side / Adjacent side
Thus, cot A in terms of tan A is given by,
cot A = 1 / tan A = 1 / (a / b) = b / a
Thus, we can say that the trigonometric ratios cot and tan has a reciprocal relationship among them.
Now, let's express cot A in terms of sin A and cos A.
We know that,
tan A = sin A / cos A
Thus,
cot A = cos A / sin A = (b/c) / (a/c) = b / a (Since, cot x = 1 / tan x)
Solved Examples using Cotangent Formula

Example 1:
If the side lengths of a rightangled triangle ABC is 13 units, 12 units, and 5 units, find the value of cot A.
Solution:
:
Using cotangent formula,
cot A = Side adjacent to angle A / Side opposite to angle A
= AC / BC = 12 / 5
Answer: cot A = 12 / 5

Example 2: Find cot P if tan P = 4 / 3.
Solution: Using the cotangent formula we know that,
cot P = 1 / tan P
= 1 / (4 / 3)
= 3 / 4
Answer: cot P = 3 / 4