Search results
Results From The WOW.Com Content Network
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
In recent literature the arctangent series is sometimes called the Mādhava–Gregory series to recognize Mādhava's priority (see also Mādhava series). [3] The special case of the arctangent of is traditionally called the Leibniz formula for π, or recently sometimes the Mādhava–Leibniz formula:
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
This article uses the standard notation ISO 80000-2, which supersedes ISO 31-11, for spherical coordinates (other sources may reverse the definitions of θ and φ): . The polar angle is denoted by [,]: it is the angle between the z-axis and the radial vector connecting the origin to the point in question.
Since the arctangent of one has a very slow convergence rate if we find two complex numbers that when multiplied will result in the same real and imaginary part we will have a Machin-like formula. An example is ( 2 + i ) {\textstyle (2+\mathrm {i} )} and ( 3 + i ) {\textstyle (3+\mathrm {i} )} .
Arctangent Arccotangent.svg - a nice plot of the arctangent and the arccotangent function Image title Arctangent(arctan)-function + Arccotangent(arccot)-function from Wikimedia Commons plot-range: -4.5 to 4.5 plotted with cubic bezier-curves in several intervalls the bezier-controll-points are calculated to give a very accurate result.
It calculates the angle frome the x-axis to the point (x,y). atan2 is usually implemented in programming languages like C++. from Wikimedia Commons plot-range: -4.5 to 4.5 plotted with cubic bezier-curves in several intervalls the bezier-controll-points are calculated to give a very accurate result.
In mathematics, a Madhava series is one of the three Taylor series expansions for the sine, cosine, and arctangent functions discovered in 14th or 15th century in Kerala, India by the mathematician and astronomer Madhava of Sangamagrama (c. 1350 – c. 1425) or his followers in the Kerala school of astronomy and mathematics. [1]