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ATAN2

  • Atan2
  • Arctangent function with two arguments

    mathematics, the function atan2 is the 2-argument arctangent. By definition, θ = atan2 ⁡ ( y , x ) {\displaystyle \theta =\operatorname {atan2} (y,x)} is the angle

    Atan2

    Atan2

    Atan2

  • Azimuth
  • Horizontal angle from north or other reference cardinal direction

    (cartographical coordinates): α = 180 π atan2 ⁡ ( X 2 − X 1 , Y 2 − Y 1 ) {\displaystyle \alpha ={\frac {180}{\pi }}\operatorname {atan2} (X_{2}-X_{1},Y_{2}-Y_{1})}

    Azimuth

    Azimuth

    Azimuth

  • Hue
  • Property of a color

    {atan2} (b^{*},a^{*}),} while, analogously, in CIELUV h u v = a t a n 2 ( v ∗ , u ∗ ) = a t a n 2 ( v ′ , u ′ ) , {\displaystyle h_{uv}=\mathrm {atan2}

    Hue

    Hue

    Hue

  • Color difference
  • Metric for difference between two colors

    } h 1 ′ = { 0 b 1 ∗ = 0 , a 1 ′ = 0 atan2 ( b 1 ∗ , a 1 ′ ) atan2 ( b 1 ∗ , a 1 ′ ) ≥ 360 ∘ atan2 ( b 1 ∗ , a 1 ′ ) + 360 ∘ otherwise {\displaystyle

    Color difference

    Color_difference

  • Solar azimuth angle
  • Azimuth angle of the Sun's position

    method that uses a solar azimuth formula based on the subsolar point and the atan2 function, as defined in Fortran 90, that gives an unambiguous solution without

    Solar azimuth angle

    Solar_azimuth_angle

  • One-form
  • Differential form of degree one or section of a cotangent bundle

    the atan2 function. Taking the derivative yields the following formula for the total derivative: d θ = ∂ x ( atan2 ⁡ ( y , x ) ) d x + ∂ y ( atan2 ⁡ (

    One-form

    One-form

  • Circular mean
  • Method for calculating average values

    mean using the atan2 variant of the arctangent function is α ¯ = atan2 ⁡ ( 1 n ∑ j = 1 n sin ⁡ α j , 1 n ∑ j = 1 n cos ⁡ α j ) = atan2 ⁡ ( ∑ j = 1 n sin

    Circular mean

    Circular_mean

  • IEEE 754
  • IEEE standard for floating-point arithmetic

    \arccos x} , arctan ⁡ x {\displaystyle \arctan x} , atan2 ⁡ ( y , x ) {\displaystyle \operatorname {atan2} (y,x)} sinPi ⁡ x = sin ⁡ π x {\displaystyle \operatorname

    IEEE 754

    IEEE_754

  • Astronomical coordinate systems
  • System for specifying positions of celestial objects

    south and opening positive to the west, A = − atan2 ⁡ ( y , x ) {\displaystyle A=-\operatorname {atan2} (y,x)} , where x = − sin ⁡ ( ϕ o ) cos ⁡ ( δ )

    Astronomical coordinate systems

    Astronomical coordinate systems

    Astronomical_coordinate_systems

  • Conversion between quaternions and Euler angles
  • Mathematical strategy

    [ atan2 ( 2 ( q w q x + q y q z ) , 1 − 2 ( q x 2 + q y 2 ) ) − π / 2 + 2 atan2 ( 1 + 2 ( q w q y − q x q z ) , 1 − 2 ( q w q y − q x q z ) ) atan2 (

    Conversion between quaternions and Euler angles

    Conversion_between_quaternions_and_Euler_angles

  • Euler angles
  • Description of the orientation of a rigid body

    represent the angles using atan2(y, x). For example, in the case of proper Euler angles: α = atan2 ⁡ ( Z 1 , − Z 2 ) , γ = atan2 ⁡ ( X 3 , Y 3 ) . {\displaystyle

    Euler angles

    Euler angles

    Euler_angles

  • Argument (complex analysis)
  • Angle of complex number about real axis

    function, atan2: Arg ⁡ ( x + i y ) = atan2 ⁡ ( y , x ) {\displaystyle \operatorname {Arg} (x+iy)=\operatorname {atan2} (y,\,x)} The atan2 function is

    Argument (complex analysis)

    Argument (complex analysis)

    Argument_(complex_analysis)

  • Cassini projection
  • Cylindrical equidistant map projection

    ⁡ φ sin ⁡ λ ) {\displaystyle x=\arcsin(\cos \varphi \sin \lambda )} y = atan2 ⁡ ( sin ⁡ φ , cos ⁡ φ cos ⁡ λ ) = arctan ⁡ ( tan ⁡ φ cos ⁡ λ ) restricted

    Cassini projection

    Cassini projection

    Cassini_projection

  • Great-circle distance
  • Shortest distance between two points on the surface of a sphere

    \end{aligned}}} where ⁠ atan2 ⁡ ( y , x ) {\displaystyle \operatorname {atan2} (y,x)} ⁠ is the two-argument arctangent. Using atan2 ensures that the correct

    Great-circle distance

    Great-circle distance

    Great-circle_distance

  • Dihedral angle
  • Angle between two planes in space

    atan2, φ = atan2 ⁡ ( u 2 ⋅ ( ( u 1 × u 2 ) × ( u 2 × u 3 ) ) , | u 2 | ( u 1 × u 2 ) ⋅ ( u 2 × u 3 ) ) . {\displaystyle \varphi =\operatorname {atan2}

    Dihedral angle

    Dihedral angle

    Dihedral_angle

  • Inverse trigonometric functions
  • Inverse functions of sin, cos, tan, etc.

    } The two-argument atan2 function computes the arctangent of y/x given y and x, but with a range of (−π, π]. In other words, atan2(y, x) is the angle

    Inverse trigonometric functions

    Inverse trigonometric functions

    Inverse_trigonometric_functions

  • Polar coordinate system
  • Coordinates comprising a distance and an angle

    φ = atan2 ⁡ ( y , x ) , {\displaystyle {\begin{aligned}r&={\sqrt {x^{2}+y^{2}}}\\\varphi &=\operatorname {atan2} (y,x),\end{aligned}}} where atan2 is a

    Polar coordinate system

    Polar coordinate system

    Polar_coordinate_system

  • Colorfulness
  • Perceived intensity of a specific color

    C_{ab}^{*}={\sqrt {a^{*2}+b^{*2}}}} h a b = atan2 ⁡ ( b ⋆ , a ⋆ ) {\displaystyle h_{ab}=\operatorname {atan2} \left({b^{\star }},{a^{\star }}\right)} and

    Colorfulness

    Colorfulness

    Colorfulness

  • N-sphere
  • Generalized sphere of dimension n (mathematics)

    1 2 , φ 1 = atan2 ⁡ ( x n 2 + x n − 1 2 + ⋯ + x 2 2 , x 1 ) , φ 2 = atan2 ⁡ ( x n 2 + x n − 1 2 + ⋯ + x 3 2 , x 2 ) , ⋮ φ n − 2 = atan2 ⁡ ( x n 2 + x

    N-sphere

    N-sphere

    N-sphere

  • Rotation formulations in three dimensions
  • Ways to represent 3D rotations

    follows: ϕ = atan2 ⁡ ( A 31 , A 32 ) θ = arccos ⁡ ( A 33 ) ψ = − atan2 ⁡ ( A 13 , A 23 ) {\displaystyle {\begin{aligned}\phi &=\operatorname {atan2} \left(A_{31}

    Rotation formulations in three dimensions

    Rotation_formulations_in_three_dimensions

  • Sobel operator
  • Image edge detection algorithm

    vertical edge which is lighter on the right side (for atan2 {\displaystyle \operatorname {atan2} } see atan2). Since the intensity function of a digital image

    Sobel operator

    Sobel operator

    Sobel_operator

  • Oklab color space
  • Standard color space with color-opponent values

    follows: C = a 2 + b 2 , h = atan2 ⁡ ( b , a ) , {\displaystyle {\begin{aligned}C&={\sqrt {a^{2}+b^{2}}},\\h&=\operatorname {atan2} (b,a),\end{aligned}}} and

    Oklab color space

    Oklab color space

    Oklab_color_space

  • Euler's formula
  • Complex exponential in terms of sine and cosine

    \textstyle r=|z|={\sqrt {x^{2}+y^{2}}}} is the magnitude of z and φ = arg z = atan2(y, x). φ is the argument of z, i.e., the angle between the x axis and the

    Euler's formula

    Euler's formula

    Euler's_formula

  • Axis–angle representation
  • Parameterization of a rotation into a unit vector and angle

    of the rotation angle uses the atan2 function: θ = 2 atan2 ⁡ ( | v | , r ) , {\displaystyle \theta =2\operatorname {atan2} (|\mathbf {v} |,r)\,,} where

    Axis–angle representation

    Axis–angle representation

    Axis–angle_representation

  • Mean anomaly
  • Specifies the orbit of an object in space

    in radians: M = atan2 ⁡ ( 1 − e 2 sin ⁡ ν , e + cos ⁡ ν ) − e 1 − e 2 sin ⁡ ν 1 + e cos ⁡ ν {\displaystyle M=\operatorname {atan2} \left({\sqrt {1-e^{2}}}\sin

    Mean anomaly

    Mean anomaly

    Mean_anomaly

  • Sunset
  • Daily falling of the Sun below the horizon

    application and extension of a formula based on the subsolar point and atan2 function. Renewable Energy, 172, 1333-1340. DOI: https://doi.org/10.1016/j

    Sunset

    Sunset

    Sunset

  • Double-precision floating-point format
  • 64-bit computer number format

    single precision. Additionally, many mathematical functions (e.g., sin, cos, atan2, log, exp and sqrt) need more computations to give accurate double-precision

    Double-precision floating-point format

    Double-precision_floating-point_format

  • Hoc (programming language)
  • if ($2<0){ return -PI/2 } else { print "atan2 domain error" return 0 } } atan2(2,3) 0.982794 atan2(0,0) atan2 domain error 0.0 Kernighan, Brian W.; Pike

    Hoc (programming language)

    Hoc_(programming_language)

  • NaN
  • Value for unrepresentable data

    forms atan2 ⁡ ( ± 0 , ± 0 ) {\displaystyle \operatorname {atan2} (\pm 0,\pm 0)} and atan2 ⁡ ( ± ∞ , ± ∞ ) {\displaystyle \operatorname {atan2} (\pm \infty

    NaN

    NaN

    NaN

  • Del in cylindrical and spherical coordinates
  • Mathematical gradient operator in certain coordinate systems

    and the projection of the radial vector onto the xy-plane. The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing

    Del in cylindrical and spherical coordinates

    Del_in_cylindrical_and_spherical_coordinates

  • Canny edge detector
  • Image edge detection algorithm

    _{x}}^{2}+{\mathbf {G} _{y}}^{2}}}} Θ = atan2 ⁡ ( G y , G x ) {\displaystyle \mathbf {\Theta } =\operatorname {atan2} \left(\mathbf {G} _{y},\mathbf {G} _{x}\right)}

    Canny edge detector

    Canny edge detector

    Canny_edge_detector

  • Sunrise
  • Time of day when the sun appears above the horizon

    application and extension of a formula based on the subsolar point and atan2 function. Renewable Energy, 172, 1333-1340. DOI: https://doi.org/10.1016/j

    Sunrise

    Sunrise

    Sunrise

  • Principal value
  • Specific values of a multivalued function

    \pi ]} For example, many computing systems include an atan2(y, x) function. The value of atan2(imaginary_part(z), real_part(z)) will be in the interval

    Principal value

    Principal_value

  • Argument of periapsis
  • Specifies the orbit of an object in space

    two-dimensional case: ω = a t a n 2 ( e y , e x ) {\displaystyle \omega =\mathrm {atan2} \left(e_{y},e_{x}\right)} If the orbit is clockwise (i.e. (r × v)z < 0)

    Argument of periapsis

    Argument of periapsis

    Argument_of_periapsis

  • CIELUV
  • Color space

    {(u^{*})^{2}+(v^{*})^{2}}},} h u v = atan2 ⁡ ( v ∗ , u ∗ ) , {\displaystyle h_{uv}=\operatorname {atan2} (v^{*},u^{*}),} where atan2 function, a "two-argument arctangent"

    CIELUV

    CIELUV

  • Geodetic coordinates
  • Geographic coordinate system

    and h are mutually involved through N: λ = atan2 ⁡ ( Y , X ) {\displaystyle \lambda =\operatorname {atan2} (Y,X)} . h = p cos ⁡ ϕ − N , {\displaystyle

    Geodetic coordinates

    Geodetic coordinates

    Geodetic_coordinates

  • HSL and HSV
  • Alternative representations of the RGB color model

    \sin(60^{\circ })={\tfrac {\sqrt {3}}{2}}(G-B)} H 2 = atan2 ⁡ ( β , α ) {\displaystyle H_{2}=\operatorname {atan2} (\beta ,\alpha )} C 2 = gmean ⁡ ( α , β ) =

    HSL and HSV

    HSL and HSV

    HSL_and_HSV

  • Universal joint
  • Mechanism with bendable rotation axis

    explicit solution using the atan2(y,x) function will be valid for − π < γ 1 < π {\displaystyle -\pi <\gamma _{1}<\pi } : γ 2 = atan2 ⁡ ( sin ⁡ γ 1 , cos ⁡ β

    Universal joint

    Universal joint

    Universal_joint

  • Libfixmath
  • Platform-independent fixed-point math library

    software 3D graphics library called FGL. For the most intensive function (atan2) benchmark results show the following results: Note: These results were

    Libfixmath

    Libfixmath

  • Complex logarithm
  • Logarithm of a complex number

    {\displaystyle (-\pi ,\pi ]} , which is expressed as atan2 ⁡ ( y , x ) {\displaystyle \operatorname {atan2} (y,x)} . This leads to the following formula for

    Complex logarithm

    Complex logarithm

    Complex_logarithm

  • Cylindrical coordinate system
  • Coordinates comprising two distances and an angle

    perform a case analysis as above. For example, this function is called by atan2(y, x) in the C programming language, and (atan y x) in Common Lisp. Spherical

    Cylindrical coordinate system

    Cylindrical coordinate system

    Cylindrical_coordinate_system

  • Subsolar point
  • Point which the sun is directly overhead

    application and extension of a formula based on the subsolar point and atan2 function". Renewable Energy. 172: 1333–1340. Bibcode:2021REne..172.1333Z

    Subsolar point

    Subsolar point

    Subsolar_point

  • Ascendant
  • Astrological sign on the eastern horizon at birth

    quadrant can be determined if calculator or programming software has the atan2(y,x) math function[further explanation needed] and then using the last rule

    Ascendant

    Ascendant

    Ascendant

  • Heaviside step function
  • Indicator function of positive numbers

    arctangent: H ( x ) =: lim ϵ → 0 + atan2 ( ϵ , − x ) π {\displaystyle H(x)=:\lim _{\epsilon \to 0^{+}}{\frac {{\mbox{atan2}}(\epsilon ,-x)}{\pi }}} A hyperfunction:

    Heaviside step function

    Heaviside step function

    Heaviside_step_function

  • JavaScript syntax
  • Set of rules defining correctly structured programs

    {\displaystyle -\pi /2} ⁠ to ⁠ + π / 2 {\displaystyle +\pi /2} ⁠) Math.atan2(-3.7, -3.7) −2.3562 rad = −135° Whole circle arctangent (⁠ − π {\displaystyle

    JavaScript syntax

    JavaScript syntax

    JavaScript_syntax

  • Quaternions and spatial rotation
  • Correspondence between quaternions and 3D rotations

    =2\operatorname {atan2} &\left({\sqrt {q_{i}^{2}+q_{j}^{2}+q_{k}^{2}}},\,q_{r}\right),\end{aligned}}} where atan2 {\displaystyle \operatorname {atan2} } is the

    Quaternions and spatial rotation

    Quaternions_and_spatial_rotation

  • CORDIC
  • Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions

    floating point operation. from math import atan2, sqrt, sin, cos, radians ITERS = 16 theta_table = [atan2(1, 2**i) for i in range(ITERS)] def compute_K(n):

    CORDIC

    CORDIC

    CORDIC

  • Exponentiation
  • Arithmetic operation

    {a^{2}+b^{2}}}} and θ = atan2 ⁡ ( b , a ) {\displaystyle \theta =\operatorname {atan2} (b,a)} , where ⁠ atan2 {\displaystyle \operatorname {atan2} } ⁠ is the two-argument

    Exponentiation

    Exponentiation

    Exponentiation

  • Eccentric anomaly
  • Angle defining a position in an orbit

    numerator and denominator, so that E can be most easily found using an atan2 function. Angle E is therefore the adjacent angle of a right triangle with

    Eccentric anomaly

    Eccentric_anomaly

  • Position of the Sun
  • Calculating the Sun's location in the sky at a given time and place

    quadrant on computer programs use double argument Arctan function such as ATAN2(y,x) α = arctan ⁡ 2 ( cos ⁡ ϵ sin ⁡ λ , cos ⁡ λ ) {\displaystyle \alpha

    Position of the Sun

    Position of the Sun

    Position_of_the_Sun

  • Geographic coordinate conversion
  • Overview of GPS conversion formulas

    coordinates to longitude is: λ = atan2 ⁡ ( Y , X ) {\displaystyle \lambda =\operatorname {atan2} (Y,X)} . where atan2 is the quadrant-resolving arc-tangent

    Geographic coordinate conversion

    Geographic_coordinate_conversion

  • Stokes parameters
  • Set of values that describe the polarization state of electromagnetic radiation

    2 , θ = 1 2 atan2 ⁡ ( U , Q ) . {\displaystyle {\begin{aligned}|L|&={\sqrt {Q^{2}+U^{2}}},\\\theta &={\frac {1}{2}}\operatorname {atan2} (U,Q).\\\end{aligned}}}

    Stokes parameters

    Stokes parameters

    Stokes_parameters

  • Great-circle navigation
  • Flight or sailing route along the shortest path between two points on a globe's surface

    the numerator and denominator in the tangent formulas (e.g., using the atan2 function). The central angle between the two points, σ12, is given by tan

    Great-circle navigation

    Great-circle navigation

    Great-circle_navigation

  • Orthographic map projection
  • Azimuthal perspective map projection

    }{R}}\end{aligned}}} For computation of the inverse formulas the use of the two-argument atan2 form of the inverse tangent function (as opposed to atan) is recommended

    Orthographic map projection

    Orthographic map projection

    Orthographic_map_projection

  • Julia set
  • Fractal sets in complex dynamics of mathematics

    (zx * zx + zy * zy) ^ (n / 2) * cos(n * atan2(zy, zx)) + cx; zy = (zx * zx + zy * zy) ^ (n / 2) * sin(n * atan2(zy, zx)) + cy; zx = xtmp; iteration = iteration

    Julia set

    Julia set

    Julia_set

  • Multibrot set
  • Construct in mathematics

    xtmp=x^5-10*x^3*y^2+5*x*y^4 + a y=5*x^4*y-10*x^2*y^3+y^5 + b x=xtmp xtmp=(x*x+y*y)^(n/2)*cos(n*atan2(y,x)) + a y=(x*x+y*y)^(n/2)*sin(n*atan2(y,x)) + b x=xtmp

    Multibrot set

    Multibrot set

    Multibrot_set

  • Additive synthesis
  • Sound synthesis technique

    atan2 ⁡ ( b k , a k ) {\displaystyle \phi _{k}=\operatorname {atan2} (b_{k},a_{k})} is the phase offset of the k {\displaystyle k} th harmonic. atan2

    Additive synthesis

    Additive_synthesis

  • Ellipse
  • Plane curve

    {2AE-BD}{B^{2}-4AC}},\\[5mu]\theta &={\tfrac {1}{2}}\operatorname {atan2} (-B,\,C-A),\end{aligned}}} where atan2 is the 2-argument arctangent function. Using trigonometric

    Ellipse

    Ellipse

    Ellipse

  • Tangent lines to circles
  • Line which touches a circle at exactly one point

    atan2 ( y 2 − y 1 , x 2 − x 1 ) β = ∓ arcsin ⁡ ( R − r ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 ) {\displaystyle {\begin{aligned}\gamma &=-{\text{atan2}}\left({y_{2}-y_{1}}

    Tangent lines to circles

    Tangent_lines_to_circles

  • Rotation matrix
  • Matrix representing a Euclidean rotation

    numerical problems: in extracting the angle, a two-argument arctangent with atan2(sin θ, cos θ) equal to θ avoids the insensitivity of arccos; and in computing

    Rotation matrix

    Rotation_matrix

  • Carbon nanotube
  • Allotropes of carbon with a cylindrical nanostructure

    vector (x,y); a function that is available in many programming languages as atan2(y,x). Conversely, given c and α, one can get the type (n,m) by the formulas:

    Carbon nanotube

    Carbon nanotube

    Carbon_nanotube

  • Solar zenith angle
  • Angle between the zenith and the centre of the Sun's disc

    application and extension of a formula based on the subsolar point and atan2 function. Renewable Energy, 172, 1333-1340. DOI: https://doi.org/10.1016/j

    Solar zenith angle

    Solar_zenith_angle

  • Instantaneous phase and frequency
  • Electrical engineering concept

    arg without concern of phase unwrapping. φ ( t ) = arg ⁡ { s a ( t ) } = atan2 ⁡ ( I m [ s a ( t ) ] , R e [ s a ( t ) ] ) + 2 m 1 π = arctan ⁡ ( I m [

    Instantaneous phase and frequency

    Instantaneous phase and frequency

    Instantaneous_phase_and_frequency

  • Edge detection
  • Image processing method

    gradient orientation can be estimated as θ = atan2 ⁡ ( L y , L x ) . {\displaystyle \theta =\operatorname {atan2} (L_{y},L_{x}).} Other first-order difference

    Edge detection

    Edge_detection

  • Sun path
  • Arc-like path that the Sun appears to follow across the sky

    application and extension of a formula based on the subsolar point and atan2 function. Renewable Energy, 172, 1333-1340. DOI: https://doi.org/10.1016/j

    Sun path

    Sun path

    Sun_path

  • Complex plane
  • Geometric representation of the complex numbers

    terms of the complete arctangent can be found at the description of the atan2 function. All the familiar properties of the complex exponential function

    Complex plane

    Complex plane

    Complex_plane

  • Atan
  • Topics referred to by the same term

    dictionary. Atan may refer to: arctangent (atan), a trigonometric function atan2, the two-argument function implementing the arctangent in many computer

    Atan

    Atan

  • Transmission line
  • Cable or other structure for carrying radio waves

    and with ψ   ≡   1 2 atan2 ⁡ ( b , a ) {\displaystyle \psi ~\equiv ~{\tfrac {1}{2}}\operatorname {atan2} (b,a)\,} where atan2 is the everywhere-defined

    Transmission line

    Transmission line

    Transmission_line

  • C mathematical functions
  • C standard library header file

    asin computes arc sine acos computes arc cosine atan computes arc tangent atan2 computes arc tangent, using signs to determine quadrants Hyperbolic functions

    C mathematical functions

    C_mathematical_functions

  • Fourier series
  • Decomposition of periodic functions

    atan2 ⁡ ( b n , a n ) = − Arg ⁡ ( c n ) {\displaystyle A_{n}={\sqrt {a_{n}^{2}+b_{n}^{2}}}\quad {\text{and}}\quad \varphi _{n}=\operatorname {atan2}

    Fourier series

    Fourier series

    Fourier_series

  • CIECAM02
  • Color appearance model

    coordinates: h = ∠ ( a , b ) = atan2 ⁡ ( b , a ) ,   ( 0 ≤ h < 360 ∘ ) {\displaystyle h=\angle (a,b)=\operatorname {atan2} (b,a),\ (0\leq h<360^{\circ })}

    CIECAM02

    CIECAM02

    CIECAM02

  • List of mathematical abbreviations
  • arctan2 – inverse tangent function with two arguments. (Also written as atan2.) arg – argument of. arg max – argument of the maximum. arg min – argument

    List of mathematical abbreviations

    List_of_mathematical_abbreviations

  • Spherical coordinate system
  • Coordinates comprising a distance and two angles

    quadrant of (x, y), as done in the equations above. See the article on atan2. Alternatively, the conversion can be considered as two sequential rectangular

    Spherical coordinate system

    Spherical coordinate system

    Spherical_coordinate_system

  • Tan-1
  • Topics referred to by the same term

    or (tan(x))−1, is recommended. Inverse function cot−1 (disambiguation) atan2 This disambiguation page lists articles associated with the same title formed

    Tan-1

    Tan-1

  • Test functions for optimization
  • Functions used to evaluate optimization algorithms

    {1}{4}}\cos 3t-{\frac {1}{8}}\cos 4t\right]^{2}+[2\sin t]^{2}} where: t = Atan2(x,y) f ( 2.0052938 , 1.1944509 ) = − 2.0239884 {\displaystyle f(2.0052938

    Test functions for optimization

    Test_functions_for_optimization

  • N-vector
  • \arctan(y/x)} should be implemented using a call to atan2(y,x). The Pole singularity of longitude is evident as atan2(0,0) is undefined. Note that the equations

    N-vector

    N-vector

  • Prewitt operator
  • Discrete differentiation operator used in image processing

    calculate the gradient's direction: Θ = atan2 ⁡ ( G y , G x ) {\displaystyle \mathbf {\Theta } =\operatorname {atan2} \left({\mathbf {G} _{y},\mathbf {G}

    Prewitt operator

    Prewitt_operator

  • Analemma
  • Diagrammatic representation of Sun's position over a period of time

    application and extension of a formula based on the subsolar point and atan2 function". Renewable Energy. 172. Elsevier BV: 1333–1340. Bibcode:2021REne

    Analemma

    Analemma

    Analemma

  • Outline of trigonometry
  • Overview of and topical guide to trigonometry

    Secant (trigonometric function), Cosecant – see Trigonometric function atan2 cis—see Euler's formula Cofunction Exsecant Gudermannian function Inverse

    Outline of trigonometry

    Outline of trigonometry

    Outline_of_trigonometry

  • Paden–Kahan subproblems
  • Set of solved geometric problems

    may be found using the atan2 function: θ = a t a n 2 ( ω T ( u ′ × v ′ ) , u ′ T v ′ ) . {\displaystyle \theta =\mathrm {atan2} (\omega ^{T}(u'\times

    Paden–Kahan subproblems

    Paden–Kahan_subproblems

  • Orbital elements
  • Parameters that define a specific orbit

    }}~.\end{aligned}}} The quadrant of the solution can be resolved using an atan2(y, x) function. True longitude can be found using the true anomaly and longitude

    Orbital elements

    Orbital_elements

  • Scale-invariant feature transform
  • Feature detection algorithm in computer vision

    y ) − L ( x − 1 , y ) ) {\displaystyle \theta \left(x,y\right)=\mathrm {atan2} \left(L\left(x,y+1\right)-L\left(x,y-1\right),L\left(x+1,y\right)-L\left(x-1

    Scale-invariant feature transform

    Scale-invariant_feature_transform

  • Gudermannian function
  • Mathematical function relating circular and hyperbolic functions

    sure to use the 2-argument arctangent, u = atan2 ⁡ ( sinh ⁡ x , cos ⁡ y ) {\textstyle u=\operatorname {atan2} (\sinh x,\cos y)} .) Likewise, if x + i y

    Gudermannian function

    Gudermannian function

    Gudermannian_function

  • Log-polar coordinates
  • Coordinate system in two dimensions

    y 2 ) , θ = atan2 ⁡ ( y , x ) . {\displaystyle {\begin{cases}\rho =\ln \left({\sqrt {x^{2}+y^{2}}}\right),\\\theta =\operatorname {atan2} (y,\,x).\end{cases}}}

    Log-polar coordinates

    Log-polar_coordinates

  • Equation of the center
  • \nu } to "eccentric anomaly": E = atan2 ⁡ (   1 − e 2 sin ⁡ ν ,   e + cos ⁡ ν ) {\displaystyle E=\operatorname {atan2} \left(\ {\sqrt {1-e^{2}}}\sin \nu

    Equation of the center

    Equation of the center

    Equation_of_the_center

  • Snellius–Pothenot problem
  • Problem in trigonometry

    {\displaystyle \phi ={\mathsf {atan2}}\left({\overline {BC}}\sin \alpha ,\ {\overline {AC}}\sin \beta \right),} where atan2 is a computer function, also

    Snellius–Pothenot problem

    Snellius–Pothenot problem

    Snellius–Pothenot_problem

  • Limaçon trisectrix
  • Quartic plane curve

    {1}{-k}}} and ϕ = a t a n 2 ( 1 , − k ) {\displaystyle \phi =atan2(1,-k)} . (Note: atan2(y,x) gives the polar angle of the Cartesian coordinate point

    Limaçon trisectrix

    Limaçon trisectrix

    Limaçon_trisectrix

  • TSL color space
  • straightforward: T = { 0.5 − atan2 ⁡ ( g ′ , r ′ ) 2 π , if   g ′ ≠ 0 0 , if   g ′ = 0 {\textstyle T={\begin{cases}0.5-{\frac {\operatorname {atan2} (g',r')}{2\pi }}

    TSL color space

    TSL_color_space

  • Kepler orbit
  • Celestial orbit whose trajectory is a conic section in the orbital plane

    computation of arg ⁡ ( x , y ) {\displaystyle \arg(x,y)} the standard function ATAN2(y,x) (or in double precision DATAN2(y,x)) available in for example the programming

    Kepler orbit

    Kepler orbit

    Kepler_orbit

  • Pythagorean addition
  • Hypotenuse of right triangle from its sides

    its implementation as the hypot function) is often used together with the atan2 function (a two-parameter form of the arctangent) to convert from Cartesian

    Pythagorean addition

    Pythagorean addition

    Pythagorean_addition

  • List of SQL reserved words
  • SQL-2023 DB2 Mimer — — — — Teradata ATAN SQL-2023 — — — — — — Teradata ATAN2 — — — — — — — Teradata ATANH — — — — — — — Teradata ATOMIC SQL-2023 — Mimer

    List of SQL reserved words

    List_of_SQL_reserved_words

  • Vincenty's formulae
  • Methods in geodesy

    second equation is indeterminate. If the standard 2-argument arctangent atan2 function is used, then these values are usually handled correctly.[clarification

    Vincenty's formulae

    Vincenty's_formulae

  • Earth section paths
  • Plane curved by the intersection of an earth ellipsoid and a plane

    two-argument arctangent function, α = atan2 ⁡ ( t ⋅ e ^ , t ⋅ n ^ ) {\displaystyle \alpha =\operatorname {atan2} (\mathbf {t} \cdot \mathbf {\hat {e}}

    Earth section paths

    Earth section paths

    Earth_section_paths

  • List of logarithmic identities
  • value is restricted to (−π, π]. It can be computed using Arg(x + iy) = atan2(y, x). Log(z) is the principal value of the complex logarithm function and

    List of logarithmic identities

    List_of_logarithmic_identities

  • Parallactic angle
  • trigonometry.) The values of sin z and of cos φ are positive, so using atan2 functions one may divide both expressions through these without losing signs;

    Parallactic angle

    Parallactic_angle

  • List of common coordinate transformations
  • {x}{x^{2}+y^{2}}}&0\\\end{pmatrix}}\end{aligned}}} See also the article on atan2 for how to elegantly handle some edge cases. So for the element: d ρ d θ

    List of common coordinate transformations

    List_of_common_coordinate_transformations

  • Navigational algorithms
  • (6) rho = sqr (x * x+y * y) r = sqr (rho * rho+z * z) lambda = atan2 (y, x) beta = atan2 (z, rho) if (z <0 #) then beta = beta - TWOPI yf rho = 0 # then

    Navigational algorithms

    Navigational algorithms

    Navigational_algorithms

  • General Perspective projection
  • Azimuthal perspective map projection

    quadrant. For computation of the inverse formulas the use of the two-argument atan2 form of the inverse tangent function (as opposed to atan) is recommended

    General Perspective projection

    General Perspective projection

    General_Perspective_projection

  • Fortran 95 language features
  • 1995 edition of the Fortran programming language standard

    and trigonometric functions SQRT EXP LOG LOG10 SIN COS TAN ASIN ACOS ATAN ATAN2 SINH COSH TANH Complex numbers: AIMAG CONJG The following are for characters:

    Fortran 95 language features

    Fortran_95_language_features

  • Reflection lines
  • v_{p})}} where a r c t a n ( y , x ) {\displaystyle arctan(y,x)} is the atan2 function producing a number in the range ( − π , π ] {\displaystyle (-\pi

    Reflection lines

    Reflection lines

    Reflection_lines

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Online names & meanings

  • Nakulesh | நாகுலேஷ
  • Boy/Male

    Tamil

    Nakulesh | நாகுலேஷ

  • YarMuhammad
  • Boy/Male

    Arabic, Muslim

    YarMuhammad

    Friend of the Prophet Muhammad

  • Abi
  • Biblical

    Abi

    my father,my father is Jehovah

  • Abd er Rahman
  • Boy/Male

    Arabic

    Abd er Rahman

    Servant of the merciful one.

  • Ashhar
  • Boy/Male

    Arabic, Muslim

    Ashhar

    Famous; Popular

  • GOGA
  • Male

    Russian

    GOGA

    (Гога) Russian Georgi, GOGA means "earth-worker, farmer."

  • Shiku
  • Girl/Female

    Indian

    Shiku

    Basket

  • Kashwin | கஷ்வீந
  • Boy/Male

    Tamil

    Kashwin | கஷ்வீந

    Star

  • Shuneal
  • Boy/Male

    Arabic, Muslim

    Shuneal

    Traveller

  • Wendel
  • Boy/Male

    American, Australian, British, Christian, English, German, Swedish, Teutonic

    Wendel

    A Wend; Wanderer

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