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  2. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    The Pythagorean trigonometric identity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms of trigonometric functions. Along with the sum-of-angles formulae , it is one of the basic relations between the sine and cosine functions.

  3. List of trigonometric identities - Wikipedia

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

    Proof of the sum-and-difference-to-product cosine identity for prosthaphaeresis calculations using an isosceles triangle. The product-to-sum identities [28] or prosthaphaeresis formulae can be proven by expanding their right-hand sides using the angle addition theorems.

  4. Proofs of trigonometric identities - Wikipedia

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

    There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.

  5. Identity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Identity_(mathematics)

    Visual proof of the Pythagorean identity: for any angle , the point (,) = (⁡, ⁡) lies on the unit circle, which satisfies the equation + =.Thus, ⁡ + ⁡ =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...

  6. Xuan tu - Wikipedia

    en.wikipedia.org/wiki/Xuan_tu

    Xuan tu or Hsuan thu (simplified Chinese: 弦图; traditional Chinese: 絃圖; pinyin: xuántú; Wade–Giles: hsüan 2 tʻu 2) is a diagram given in the ancient Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. [1] Zhoubi Suanjing is one of the oldest Chinese texts on mathematics. The ...

  7. Students discover and publish unexpected proof for 2,000-year ...

    www.aol.com/students-discover-publish-unexpected...

    Ne’Kiya Jackson and Calcea Johnson have published a paper on a new way to prove the 2000-year-old Pythagorean theorem. Their work began in a high school math contest.

  8. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Trigonometric identities mnemonic. Another mnemonic permits all of the basic identities to be read off quickly. The hexagonal chart can be constructed with a little thought: [10] Draw three triangles pointing down, touching at a single point. This resembles a fallout shelter trefoil. Write a 1 in the middle where the three triangles touch

  9. Play Hearts Online for Free - AOL.com

    www.aol.com/games/play/masque-publishing/hearts

    Enjoy a classic game of Hearts and watch out for the Queen of Spades!