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  2. Conversion between quaternions and Euler angles - Wikipedia

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

    A direct formula for the conversion from a quaternion to Euler angles in any of the 12 possible sequences exists. [2] For the rest of this section, the formula for the sequence Body 3-2-1 will be shown. If the quaternion is properly normalized, the Euler angles can be obtained from the quaternions via the relations:

  3. List of trigonometric identities - Wikipedia

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

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  4. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle.Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the unit hyperbola.

  5. List of formulas in Riemannian geometry - Wikipedia

    en.wikipedia.org/wiki/List_of_formulas_in...

    The variation formula computations above define the principal symbol of the mapping which sends a pseudo-Riemannian metric to its Riemann tensor, Ricci tensor, or ...

  6. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides a , {\displaystyle a,} b , {\displaystyle b,} and c , {\displaystyle c,} opposite respective angles α , {\displaystyle \alpha ,} β , {\displaystyle ...

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  8. Stanley recalls 2.6 million mugs after reports of burns from ...

    www.aol.com/news/stanley-recalls-2-6-million...

    Stanley is recalling 2.6 million mugs sold in the U.S. after the company received dozens of consumer complaints, including some users who reported getting burned and requiring medical attention ...

  9. Daughter gifts dad an image composed of daily text messages ...

    www.aol.com/news/daughter-gifts-dad-image...

    A woman who saved years' worth of daily text messages from her dad turned them into a sentimental Christmas gift that left her dad in tears. Leah Doherty of Ohio told "Good Morning America" that ...