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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. List of trigonometric identities - Wikipedia

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

    The half-angle formula for cosine can be obtained by replacing with / and taking the square-root of both sides: ⁡ (/) = (+ ⁡) /. Sine power-reduction formula: an illustrative diagram. The shaded blue and green triangles, and the red-outlined triangle E B D {\displaystyle EBD} are all right-angled and similar, and all contain the angle θ ...

  4. File:Tangent half-angle formula.svg - Wikipedia

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

    File:Tangent half-angle formula.svg. Add languages. Page contents not supported in other languages. File; Talk; ... Download QR code; In other projects ...

  5. 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 ...

  6. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    A trigonometry table is essentially a reference chart that presents the values of sine, cosine, tangent, and other trigonometric functions for various angles. These angles are usually arranged across the top row of the table, while the different trigonometric functions are labeled in the first column on the left.

  7. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    Repeated application of the half-angle formulas leads to nested radicals, specifically nested square roots of 2 of the form . In general, the sine and cosine of most angles of the form β / 2 n {\displaystyle \beta /2^{n}} can be expressed using nested square roots of 2 in terms of β {\displaystyle \beta } .

  8. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The formulas for addition and subtraction involving a small angle may be used for interpolating between trigonometric table values: Example: sin(0.755) ⁡ = ⁡ (+) ⁡ + ⁡ () + () where the values for sin(0.75) and cos(0.75) are obtained from trigonometric table. The result is accurate to the four digits given.

  9. Proofs of trigonometric identities - Wikipedia

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

    For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number, except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°). Referring to the diagram at the right, the six ...

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