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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. 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. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The quantity 206 265 ″ is approximately equal to the number of arcseconds in a circle (1 296 000 ″), divided by 2π, or, the number of arcseconds in 1 radian. The exact formula is = ⁡ (″) and the above approximation follows when tan X is replaced by X.

  5. Pythagorean trigonometric identity - Wikipedia

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

    The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity involving the cotangent and the cosecant also follows from the Pythagorean theorem.

  6. 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.

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  8. NFL commissioner Roger Goodell says league will aim for 8 ...

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    After games in Brazil, the United Kingdom and Germany this season, the NFL plans to keep on growing its international footprint. NFL commissioner Roger Goodell said Sunday that the league is ...

  9. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    To prove the law of tangents one can start with the law of sines: a sin ⁡ α = b sin ⁡ β = d , {\displaystyle {\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}=d,} where ⁠ d {\displaystyle d} ⁠ is the diameter of the circumcircle , so that ⁠ a = d sin ⁡ α {\displaystyle a=d\sin \alpha } ⁠ and ⁠ b = d sin ⁡ β {\displaystyle ...