Arctan, short for arc tangent, is a mathematical function used to determine the angle whose tangent is a given number or ratio. It is the inverse function of the tangent function. The arctan function is defined for real numbers and returns angles in radians.
The arctan function is often denoted as atan(x) or tan^(-1)(x), where x is the input value. It takes x as an argument and returns the angle in radians whose tangent is x, within the range of -π/2 to π/2. This means the output of arctan(x) lies between -90 degrees and 90 degrees.
The arctan function is commonly used in trigonometry and geometry to find angles in right-angled triangles. By inputting the ratio of the lengths of the sides of a right triangle, arctan can determine the angle opposite the given side.
Arctan can also be used in calculus to find angles of inclination or slope. It is used to find the angle between a tangent line and the x-axis at a particular point on a curve.
In programming and scientific calculators, the arctan function is typically included as a built-in function. It allows users to calculate inverse tangent values with ease and efficiency.
Overall, arctan is a fundamental mathematical function that plays a significant role in various fields, including trigonometry, geometry, calculus, and computer programming.
