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The derivative of arctan x is 1 / (1 + x 2); conversely, the integral of 1 / (1 + x 2) is arctan x. If = ...
The two figures below show 3D views of respectively atan2(y, x) and arctan( y / x ) over a region of the plane. Note that for atan2( y , x ) , rays in the X / Y -plane emanating from the origin have constant values, but for arctan( y / x ) lines in the X / Y -plane passing through the origin have constant values.
The most common convention is to name inverse trigonometric functions using an arc- prefix: arcsin(x), arccos(x), arctan(x), etc. [1] (This convention is used throughout this article.) This notation arises from the following geometric relationships: [ citation needed ] when measuring in radians, an angle of θ radians will correspond to an arc ...
The inverse tangent integral is defined by: = The arctangent is taken to be the principal branch; that is, − π /2 < arctan(t) < π /2 for all real t. [1]Its power series representation is
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
The Gudermannian function relates the area of a circular sector to the area of a hyperbolic sector, via a common stereographic projection.If twice the area of the blue hyperbolic sector is ψ, then twice the area of the red circular sector is ϕ = gd ψ.
A milliradian (SI-symbol mrad, sometimes also abbreviated mil) is an SI derived unit for angular measurement which is defined as a thousandth of a radian (0.001 radian). ). Milliradians are used in adjustment of firearm sights by adjusting the angle of the sight compared to the barrel (up, down, left, or
The table of the initial values of () (these values are also called the "figurate numbers for the n-dimensional cross polytopes" in the OEIS [6]) may illustrate the recursion formula (1), which can be taken to mean that each entry is the sum of the three neighboring entries: to its left, above and above left, e.g. () = = + +.