cot(x)
In mathematics, cot(x) stands for the cotangent function
In mathematics, cot(x) stands for the cotangent function. The cotangent function is the reciprocal of the tangent function. It is defined as the ratio of the adjacent side to the opposite side in a right triangle.
To understand cot(x) further, let’s consider a right triangle with an angle x. With respect to angle x, the cotangent of x is defined as the ratio of the length of the adjacent side to the length of the opposite side. Mathematically, it is expressed as:
cot(x) = adjacent side / opposite side
This can also be expressed in terms of the sine and cosine functions as:
cot(x) = cos(x) / sin(x)
Note that the cotangent function is not defined for certain angles, specifically when the sine function is equal to zero. In other words, the cotangent function is not defined at 90 degrees and its multiples (90°, 180°, 270°, etc.).
The cotangent function is periodic with a period of π (pi) radians or 180 degrees. It takes positive and negative values where it is defined, depending on the quadrant of the angle x.
Graphically, the cotangent function appears as a periodic wave, similar to the tan(x) function, but shifted by 90 degrees. It has vertical asymptotes at the angles where its denominator (sin(x)) is equal to zero. These vertical asymptotes occur when x is equal to 0, π, 2π, etc.
More Answers:
How to Find the Derivative of the Trigonometric Function csc(x) with Respect to xA Guide to Finding the Derivative of the Secant Function Using Quotient Rule and Trig Identities
Derivative of Cotangent Function | How to Find and Simplify the Derivative of Cot(x)