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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. Multivalued function - Wikipedia

    en.wikipedia.org/wiki/Multivalued_function

    As a consequence, arctan(1) is intuitively related to several values: π /4, 5 π /4, −3 π /4, and so on. We can treat arctan as a single-valued function by restricting the domain of tan x to − π /2 < x < π /2 – a domain over which tan x is monotonically increasing. Thus, the range of arctan(x) becomes − π /2 < y < π /2.

  4. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    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 ...

  5. Conversion between quaternions and Euler angles - Wikipedia

    en.wikipedia.org/wiki/Conversion_between...

    Note that the arctan functions implemented in computer languages only produce results between −π/2 and π/2, which is why atan2 is used to generate all the correct orientations. Moreover, typical implementations of arctan also might have some numerical disadvantages near zero and one. Some implementations use the equivalent expression: [3]

  6. Fisher transformation - Wikipedia

    en.wikipedia.org/wiki/Fisher_transformation

    The application of Fisher's transformation can be enhanced using a software calculator as shown in the figure. Assuming that the r-squared value found is 0.80, that there are 30 data [clarification needed], and accepting a 90% confidence interval, the r-squared value in another random sample from the same population may range from 0.656 to 0.888.

  7. Machin-like formula - Wikipedia

    en.wikipedia.org/wiki/Machin-like_formula

    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} )} .

  8. Arctangent series - Wikipedia

    en.wikipedia.org/wiki/Arctangent_series

    In mathematics, the arctangent series, traditionally called Gregory's series, is the Taylor series expansion at the origin of the arctangent function: [1] ⁡ = + + = = + +. This series converges in the complex disk | |, except for = (where =).

  9. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same.