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  2. atan2 - Wikipedia

    en.wikipedia.org/wiki/Atan2

    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

  3. Arctangent series - Wikipedia

    en.wikipedia.org/wiki/Arctangent_series

    The derivative of arctan x is 1 / (1 + x 2); conversely, the integral of 1 / (1 + x 2) is arctan x.. If = ⁡ then ⁡ =. The derivative is = ⁡ = + ⁡. Taking the reciprocal, = + ⁡ = +.

  4. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    For example, the derivative of the sine function is written sin ′ (a) = cos(a), meaning that the rate of change of sin(x) at a particular angle x = a is given by the cosine of that angle. All derivatives of circular trigonometric functions can be found from those of sin( x ) and cos( x ) by means of the quotient rule applied to functions such ...

  5. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    The derivatives in the table above are for when the range of the inverse secant is [,] and when the range of the inverse cosecant is [,]. It is common to additionally define an inverse tangent function with two arguments , arctan ⁡ ( y , x ) {\textstyle \arctan(y,x)} .

  6. Del in cylindrical and spherical coordinates - Wikipedia

    en.wikipedia.org/wiki/Del_in_cylindrical_and...

    The function atan2(y, x) can be used instead of the mathematical function arctan(y/x) owing to its domain and image. The classical arctan function has an image of (−π/2, +π/2), whereas atan2 is defined to have an image of (−π, π].

  7. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    In calculus, the inverse function rule is a formula that expresses the derivative of the inverse of a bijective and differentiable function f in terms of the derivative of f. ...

  8. Vector fields in cylindrical and spherical coordinates

    en.wikipedia.org/wiki/Vector_fields_in...

    Note: This page uses common physics notation for spherical coordinates, in which is the angle between the z axis and the radius vector connecting the origin to the point in question, while is the angle between the projection of the radius vector onto the x-y plane and the x axis. Several other definitions are in use, and so care must be taken ...

  9. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    Following this recommendation, the ISO 80000-2 standard abbreviations use the prefix ar-(that is: arsinh, arcosh, artanh, arsech, arcsch, arcoth). In computer programming languages, inverse circular and hyperbolic functions are often named with the shorter prefix a-(asinh, etc.). This article will consistently adopt the prefix ar-for convenience.