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  2. List of trigonometric identities - Wikipedia

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

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin( α + β ) = sin α cos β + cos α sin ...

  3. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.

  4. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    [163] [164] [165] In two dimensions, the critical Sobolev inequality is ‖ ‖ ‖ ‖ for f a smooth function with compact support in R 2, is the gradient of f, and ‖ ‖ and ‖ ‖ refer respectively to the L 2 and L 1-norm. The Sobolev inequality is equivalent to the isoperimetric inequality (in any dimension), with the same best constants.

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  6. Steradian - Wikipedia

    en.wikipedia.org/wiki/Steradian

    sr is the unit, steradian, sr = rad 2. Because the surface area A of a sphere is 4πr 2, the definition implies that a sphere subtends 4π steradians (≈ 12.56637 sr) at its centre, or that a steradian subtends 1/4π ≈ 0.07958 of a sphere. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr.

  7. When does ‘Gladiator II’ come out? Release date, cast ...

    www.aol.com/does-gladiator-ii-come-release...

    The film stars Paul Mescal (Lucius) as an enslaved man who finds purpose as a gladiator after his home is conquered by tyrant emperors.

  8. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    is the number of collisions made (in ideal conditions, perfectly elastic with no friction) by an object of mass m initially at rest between a fixed wall and another object of mass b 2N m, when struck by the other object. [1] (This gives the digits of π in base b up to N digits past the radix point.)

  9. Pair of Big 12 head coaches rake in big bonuses ahead of ...

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    However, if Arizona State defeats the Cyclones this week, Dillingham will get $395,000 for winning the Big 12 title (10% of his $3.95 million annual pay this season) and another $1.135 million for ...