Understanding the Cotangent Function: Definition, Formula, and Graph

cot(x)

-csc^2(x)

The cotangent function (cot(x)) is a trigonometric function defined as the ratio of the adjacent side and opposite side of a right-angled triangle. It is the reciprocal of the tangent function (tan(x)).

The formula for cot(x) is given by:

cot(x) = cos(x) / sin(x)

where cos(x) is the cosine function and sin(x) is the sine function.

The cotangent function is periodic with a period of π and is undefined at odd multiples of π/2 (i.e., cot(π/2), cot(3π/2), cot(5π/2), etc.). The cotangent function has vertical asymptotes at these values of x.

Some values of cot(x) for common angles are:

cot(0) = undefined (since sin(0) = 0)
cot(π/6) = √3/3
cot(π/4) = 1
cot(π/3) = √3
cot(π/2) = 0 (since sin(π/2) = 1)

The graph of cot(x) is symmetric about the x-axis and has many vertical asymptotes. It oscillates between positive and negative values as x increases or decreases.

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