Understanding the Arccotangent Function | Definition, Calculation, and Domain

cot^(-1)x or arccot(x)

The term “cot^(-1)x” or “arccot(x)” refers to the inverse trigonometric function called the arccotangent or the inverse cotangent

The term “cot^(-1)x” or “arccot(x)” refers to the inverse trigonometric function called the arccotangent or the inverse cotangent. It is denoted by “cot^(-1)x” or “arccot(x)” and is defined as the angle whose cotangent equals the given value of x.

To understand this better, let’s briefly review the cotangent function. In trigonometry, the cotangent of an angle is the ratio of the adjacent side to the opposite side in a right triangle. It can also be expressed in terms of sine and cosine as cot(theta) = cos(theta)/sin(theta).

In the case of the arccotangent, given a value of x, it represents the angle whose cotangent is equal to x. This angle is expressed in radians or degrees, depending on the system being used.

To find the value of arccot(x), you can use a scientific calculator or mathematical software that provides the arccotangent function. Simply input the value of x and evaluate the function, which will give you the angle whose cotangent is x.

For example, let’s say we want to find the angle that has a cotangent value of 2. Using the arccotangent function, we can calculate arccot(2) ≈ 0.4636 radians or approximately 26.565 degrees.

It is important to note that the arccotangent function has a restricted domain. It only provides a single value within a specified range. In the case of arccot(x), the domain is from -infinity to +infinity, but the range is limited to (0, π) or (0, 180 degrees). This means that the arccotangent function cannot produce an angle that lies outside this range.

Overall, the arccotangent function, denoted as cot^(-1)x or arccot(x), is a useful tool for finding angles when given the cotangent value of an angle.

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