Cotangent

Let's assume we have a right triangle ABC, where ∠C=90^o. Side a is adjacent to angle α, side b is opposite to angle α, and c is the hypotenuse (the longest side of the triangle).

The definition of the cotangent of angle α is:

The cotangent of an angle (cot) is the ratio of the length of the adjacent side to the opposite side.

For this example:

cot α = a/b

Example:

Assume the side lengths are:

• a = 3
• b = 4
• c = 5

1. Verify that the triangle is right-angled using the Pythagorean theorem:

Since the equality holds, it is a right triangle.

2. Calculate the cotangent of angle α:

cot α = a/b = 3/4 = 0.75

Result:

cot α = 0.75

Thus, the cotangent of angle α in this right triangle is 0.75.