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  2. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is ⁠ 1 / 2 ⁠ (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan ⁠ 1 / 2 ⁠ (a + b) = (sin a + sin b) / (cos a + cos b).

  3. Tangent half-angle substitution - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle...

    The tangent of half an angle is important in spherical trigonometry and was sometimes known in the 17th century as the half tangent or semi-tangent. [2] Leonhard Euler used it to evaluate the integral ∫ d x / ( a + b cos ⁡ x ) {\textstyle \int dx/(a+b\cos x)} in his 1768 integral calculus textbook , [ 3 ] and Adrien-Marie Legendre described ...

  4. 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.

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The sum and difference formulas allow expanding the sine, the cosine, and the tangent of a sum or a difference of two angles in terms of sines and cosines and tangents of the angles themselves. These can be derived geometrically, using arguments that date to Ptolemy. One can also produce them algebraically using Euler's formula. Sum

  6. Law of tangents - Wikipedia

    en.wikipedia.org/wiki/Law_of_tangents

    In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides. In Figure 1, a , b , and c are the lengths of the three sides of the triangle, and α , β , and γ are the angles opposite those three respective sides.

  7. List of equations in wave theory - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_wave...

    Quantity (common name/s) (Common) symbol/s SI units Dimension Number of wave cycles N: dimensionless dimensionless (Oscillatory) displacement Symbol of any quantity which varies periodically, such as h, x, y (mechanical waves), x, s, η (longitudinal waves) I, V, E, B, H, D (electromagnetism), u, U (luminal waves), ψ, Ψ, Φ (quantum mechanics).

  8. No. 14 Arizona State blows out rival Arizona 49-7 and secures ...

    www.aol.com/no-14-arizona-state-blows-000337204.html

    The Sun Devils led 35-0 at halftime behind three touchdown runs by Skattebo and barely let off the gas in the second half. Leavitt threw for 291 yards on 17-of-22 passing and Arizona State had 643 ...

  9. Outline of trigonometry - Wikipedia

    en.wikipedia.org/wiki/Outline_of_trigonometry

    Generating trigonometric tables; Āryabhaṭa's sine table; Bhaskara I's sine approximation formula; Madhava's sine table; Ptolemy's table of chords, written in the second century A.D. Rule of marteloio; Canon Sinuum, listing sines at increments of two arcseconds, published in the late 1500s