- #1
pcm
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Homework Statement
i wanted to know ,why is the range of cot-1(x) (0,π), unlike tan-1(x)
which has its range (-π/2,π/2). because for sin and cosec inverse range is same, for cos and sec inverse range is same.
pcm said:domain of cot(x) is {real numbers} - {nπ;n is integer}
pcm said:but what about cosec-1(x)?
pcm said:the attached graph shows
graph of cot-1(x) when
i)domain of cot(x) is restricted to (- π/2,π/2) (the blue discontinuous curve)
ii)domain of cot(x) is restricted to (0,π) (the continuous blue green curve)
has discontinuity got something to do with the definition of this function?
The notation "cot-1(x)" represents the inverse function of the cotangent function, also known as the arccotangent function. This function takes in a value of x as an input and returns the angle in radians whose cotangent is x.
The range of cot-1(x) is from 0 to π because the cotangent function has a period of π, meaning that its values repeat every π radians. Therefore, the inverse function has a range of one period, which is from 0 to π.
No, the range of cot-1(x) cannot be negative. Since cot-1(x) represents an angle, it can only take on values between 0 to π, which are positive angles in radians. Negative values do not make sense in this context.
The range of cot-1(x) is the inverse of the range of cot(x). This means that the values of cot-1(x) are the angles whose cotangent is x, while the values of cot(x) are the cotangents of those angles. In other words, the range of cot(x) is the domain of cot-1(x) and vice versa.
Both cot-1(x) and arctan(x) represent inverse trigonometric functions, but they are the inverse functions of different trigonometric ratios. While cot-1(x) is the inverse of cot(x), arctan(x) is the inverse of tan(x). This means that they have different ranges and their graphs look different, even though they both represent angles.