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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. Help:Displaying a formula - Wikipedia

    en.wikipedia.org/wiki/Help:Displaying_a_formula

    7.1 1 step method. 7.2 3 step method. ... \arctan j ⁡, ⁡, ⁡ \sinh k, \cosh l, \tanh m, \coth n ... The <math> tag can take a display attribute with possible ...

  4. Proofs of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/Proofs_of_trigonometric...

    For the sine function, we can handle other values. If θ > π /2, then θ > 1. But sin θ ≤ 1 (because of the Pythagorean identity), so sin θ < θ. So we have ⁡ < <. For negative values of θ we have, by the symmetry of the sine function

  5. Complex number - Wikipedia

    en.wikipedia.org/wiki/Complex_number

    The horizontal axis is generally used to display the real part, with increasing values to the right, and the imaginary part marks the vertical axis, with increasing values upwards. A complex number z, as a point (black) and its position vector (blue). A real number a can be regarded as a complex number a + 0i, whose imaginary part is 0.

  6. Subtended angle - Wikipedia

    en.wikipedia.org/wiki/Subtended_angle

    In geometry, an angle subtended (from Latin for "stretched under") by a line segment at an arbitrary vertex is formed by the two rays between the vertex and each endpoint of the segment.

  7. Mean value theorem - Wikipedia

    en.wikipedia.org/wiki/Mean_value_theorem

    Cauchy's mean value theorem, also known as the extended mean value theorem, is a generalization of the mean value theorem. [ 6 ] [ 7 ] It states: if the functions f {\displaystyle f} and g {\displaystyle g} are both continuous on the closed interval [ a , b ] {\displaystyle [a,b]} and differentiable on the open interval ( a , b ) {\displaystyle ...

  8. Austria - Wikipedia

    en.wikipedia.org/wiki/Austria

    Austria, [e] formally the Republic of Austria, [f] is a landlocked country in Central Europe, lying in the Eastern Alps. [15] It is a federation of nine states, of which the capital Vienna is the most populous city and state.

  9. Sydney Opera House - Wikipedia

    en.wikipedia.org/wiki/Sydney_Opera_House

    The achievement of this solution avoided the need for expensive formwork construction by allowing the use of precast units and it also allowed the roof tiles to be prefabricated in sheets on the ground, instead of being stuck on individually at height. The tiles themselves were manufactured by the Swedish company Höganäs Keramik. It took ...