Understanding the Cotangent Function: Definition and Explanation

cot 𝜃

The cotangent (cot) function is a trigonometric function that relates to the tangent function

The cotangent (cot) function is a trigonometric function that relates to the tangent function. It is defined as the reciprocal of the tangent function, so it can be represented as:

cot 𝜃 = 1 / tan 𝜃

To understand the cotangent function, we need to briefly review the concept of tangent. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

In the unit circle, where the radius is 1, we can define the tangent of an angle 𝜃 as the y-coordinate of a point on the unit circle divided by the x-coordinate of the same point. This gives us the formula:

tan 𝜃 = y-coordinate / x-coordinate

Now, since the cotangent is the reciprocal of the tangent, we can express cot 𝜃 as:

cot 𝜃 = 1 / (y-coordinate / x-coordinate)

To simplify this expression, we can multiply the numerator and denominator by x-coordinate. This results in:

cot 𝜃 = x-coordinate / y-coordinate

In conclusion, the cotangent of an angle 𝜃 is equal to the x-coordinate of a point on the unit circle divided by the y-coordinate of the same point. It represents the ratio of the adjacent side to the opposite side in a right triangle.

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