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  2. Proofs of trigonometric identities - Wikipedia

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

    The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...

  3. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. 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.

  4. Talk:Law of cosines/Archive 1 - Wikipedia

    en.wikipedia.org/wiki/Talk:Law_of_cosines/Archive_1

    These techniques correspond respectively to the Pythagorean and Power of Points derivations of the Law of Cosines. Replica of diagrams in Book 1, Page 21 of "De Revolutionibus Orbium Coelestium" Fig 1 and Fig 2 are replicas of the diagrams from Page 21 of De Revolutionibus Orbium Coelestium.In Fig 1 triangle ABC is drawn with B an acute angle ...

  5. File:Triangle with trigonometric proof of the law of cosines ...

    en.wikipedia.org/wiki/File:Triangle_with...

    Date/Time Thumbnail Dimensions User Comment; current: 02:01, 16 December 2007: 320 × 180 (1 KB): Ttbya {{Information |Description=Image describing the w:en:Law of cosines |Source=self-made |Date=December 16, 2007 |Permission=See below. |other_versions=Image:Triangle with trigonometric proof of the law of cosines.png}} Vectorized version of the

  6. Spherical trigonometry - Wikipedia

    en.wikipedia.org/wiki/Spherical_trigonometry

    For example, Todhunter [1] gives two proofs of the cosine rule (Articles 37 and 60) and two proofs of the sine rule (Articles 40 and 42). The page on Spherical law of cosines gives four different proofs of the cosine rule. Text books on geodesy [2] and spherical astronomy [3] give different proofs and the online resources of MathWorld provide ...

  7. File:Law of cosines in plane trigonometry.svg - Wikipedia

    en.wikipedia.org/wiki/File:Law_of_cosines_in...

    English: Image to demonstrate the law of cosines of plane trigonometry. Only one of the three equalities is shown; the other two are proved in the same way, taking the other two sides of the triangle as its base.

  8. 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 .

  9. Spherical law of cosines - Wikipedia

    en.wikipedia.org/wiki/Spherical_law_of_cosines

    If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable. [3] A variation on the law of cosines, the second spherical law of cosines, [4] (also called the cosine rule for angles [1]) states: