cot(x)
-csc^2(x)
cot(x) is the abbreviation of the cotangent function, which is defined as the reciprocal of the tangent function. Therefore, the value of cot(x) for any given angle x can be obtained by dividing 1 by the value of tangent of the same angle x.
The tangent function is defined as the ratio of the opposite side to the adjacent side in a right-angled triangle. Therefore, we can use this definition to write cot(x) in terms of sine and cosine functions as follows:
cot(x) = 1 / tan(x)
cot(x) = 1 / (sin(x) / cos(x))
cot(x) = cos(x) / sin(x)
In trigonometry, it is important to note that the cotangent function is undefined for x = kπ, where k is any integer, because in this case, the denominator sin(x) becomes zero, which is not allowed.
Furthermore, the cotangent function has a periodicity of π radians, that is, cot(x) is equal to cot(x + kπ), where k is any integer. This periodicity can be visualized using the unit circle, where the value of cot(x) is given by the x-value of the point of intersection between the corresponding angle and the vertical axis.
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