Understanding the Inverse Cotangent Function | Explained with Examples and Calculation

y = arccotx

The equation y = arccot(x) represents the inverse function of the cotangent function

The equation y = arccot(x) represents the inverse function of the cotangent function. In other words, it is the angle (in radians) whose cotangent is equal to x. The arccot(x) function is also sometimes written as arccotangent(x) or cot^-1(x).

To better understand this equation, let’s break it down:

– “arccot” stands for “arc-cotangent”. It is the inverse function of the cotangent function, denoted as cot(x).
– The cotangent function (cot(x)) is defined as the ratio of the adjacent side to the opposite side in a right triangle. Mathematically, cot(x) can be expressed as cot(x) = cos(x)/sin(x).
– “x” represents the value of the cotangent function. In the equation y = arccot(x), we are looking for the angle (y) whose cotangent is equal to x.

It is essential to note that the inverse function arccot(x) has a restricted domain. The cotangent function has a periodic behavior, and its range is (-∞, ∞). However, the arccot(x) function has a domain of (0, π), excluding 0. This means that the angle y, measured in radians, will be between 0 and π, but can never be equal to 0.

To find the value of y for a given x, you can use a scientific calculator that has the arccot(x) function or refer to trigonometric tables. Alternatively, you can also use the following steps:

1. Begin with the equation y = arccot(x).
2. Rewrite it as cot(y) = x.
3. Rearrange the equation to solve for y: y = cot^-1(x).
4. Calculate the value of y using either a calculator or trigonometric tables.

For example:
If we have x = √3/3, we want to find the angle y whose cotangent is √3/3.
1. The equation would be y = arccot(√3/3).
2. Rewrite it as cot(y) = √3/3.
3. Rearrange the equation to solve for y: y = cot^-1(√3/3).
4. Calculate the value of y, which is approximately 0.7854 radians or 45 degrees.

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