cotx
-csc^2x
The cotangent of x (cot x) is a trigonometric function that represents the ratio of the adjacent side to the opposite side of a right-angled triangle, with x being the angle between the hypotenuse and the adjacent side. It can also be expressed in terms of the tangent function of x as the reciprocal of the tangent of x.
The formula for cot x is:
cot x = cos x / sin x
Alternatively, it can be expressed as:
cot x = 1 / tan x
Here, cos x represents the adjacent side of the triangle, and sin x represents the opposite side.
It is important to note that the cotangent function is undefined for x values that make sin x equal to zero. This occurs at x = (nπ)/2, where n is an integer. Additionally, the cotangent function is periodic with a period of π, meaning that cot (x + π) = cot x.
Some common values for cot x include:
cot 0 = undefined
cot π/6 = √3/3
cot π/4 = 1
cot π/3 = √3
cot π/2 = 0
The cotangent function can be useful in various fields, including physics and engineering, in calculating angles and distances in right-angled triangles.
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