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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. 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.

  4. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...

  5. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    Thus each of these angles has a rational value for its half-angle tangent, using tan φ/2 = sin φ / (1 + cos φ). The reverse is also true. If there are two positive angles that sum to 90°, each with a rational half-angle tangent, and the third angle is a right angle then a triangle with these interior angles can be scaled to a Pythagorean ...

  6. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...

  7. Shop these 10 thoughtful gifts under $50 from Nordstrom that ...

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    This simple design also comes in black, gray, tan and beige. $41 at Nordstrom. Nordstrom. Palais des Thés Holiday Favorites Assorted Tea Gift Set.

  8. The 6 best and 6 worst celebrity Christmas albums - AOL

    www.aol.com/6-best-6-worst-celebrity-192259339.html

    Every year, celebrities try to capitalize on the holiday season by releasing festive music. Singers like Mariah Carey, Ariana Grande, and Michael Bublé managed to perfect the cheesy art form ...

  9. These are the pedophile symbols you need to know to protect ...

    www.aol.com/news/2016-04-26-these-are-the...

    Click through the see images of the symbols: Show comments. Advertisement. Advertisement. Holiday Shopping Guides. See all. AOL. Glamorous gold jewelry staples you can wear on repeat — all under ...