cot - 1 is the inverse function of cotangent. It is also known as arccotangent or arcoth. The domain of cot - 1 is (-∞, 0) U (0, ∞) and the range is (0, π). The value of cot - 1 of a number x gives the angle whose cotangent is x.
The graph of cot - 1 is a curve that starts at (-π/2, 0) and goes to (π/2, π) as x approaches infinity. The graph is odd and has a vertical asymptote at x=0.
The trigonometric identity for cot - 1 is:
cot(cot - 1(x)) = x
There are several properties of cot - 1 that are similar to other trigonometric functions. For example, cot - 1(-x) = π - cot - 1(x) and cot - 1(1/x) = π/2 - cot - 1(x).
Applications of cot - 1 can be found in fields such as engineering, physics, and navigation. It is used in solving problems related to angles and distances, such as determining the angles of elevation and depression in surveying and navigation.
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