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  2. 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.

  3. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    A trigonometric number is a number that can be expressed as the sine or cosine of a rational multiple of π radians. [2] Since sin ⁡ ( x ) = cos ⁡ ( x − π / 2 ) , {\displaystyle \sin(x)=\cos(x-\pi /2),} the case of a sine can be omitted from this definition.

  4. Tangent half-angle formula - Wikipedia

    en.wikipedia.org/wiki/Tangent_half-angle_formula

    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 tan1 / 2 ⁠ (a + b) = (sin a + sin b) / (cos a + cos b). The formulae sin ⁠ 1 / 2 ⁠ (a + b) and cos ⁠ 1 / 2 ⁠ (a + b) are the ratios of the actual distances to ...

  5. Proofs of trigonometric identities - Wikipedia

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

    Identity 1: ⁡ + ⁡ = The following two results follow from this and the ratio identities. To obtain the first, divide both sides of ⁡ + ⁡ = by ⁡; for the second, divide by ⁡.

  6. Niven's theorem - Wikipedia

    en.wikipedia.org/wiki/Niven's_theorem

    In radians, one would require that 0° ≤ x ≤ π/2, that x/π be rational, and that sin(x) be rational. The conclusion is then that the only such values are sin(0) = 0, sin(π/6) = 1/2, and sin(π/2) = 1. The theorem appears as Corollary 3.12 in Niven's book on irrational numbers. [2] The theorem extends to the other trigonometric functions ...

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  8. Download, install, or uninstall AOL Desktop Gold

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    1. Search your inbox for the subject line 'Get Started with AOL Desktop Gold'. 2. Open the email. 3. Click Download AOL Desktop Gold or Update Now. 4. Navigate to your Downloads folder and click Save. 5. Follow the installation steps listed below.

  9. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    "The amazing number π " (PDF). Nieuw Archief voor Wiskunde. 5th series. 1 (3): 254– 258. Zbl 1173.01300. Kazuya Kato, Nobushige Kurokawa, Saito Takeshi: Number Theory 1: Fermat's Dream. American Mathematical Society, Providence 1993, ISBN 0-8218-0863-X