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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. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.

  4. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    Similarly / = is a constructible angle because 12 is a power of two (4) times a Fermat prime (3). But π / 9 = 20 ∘ {\displaystyle \pi /9=20^{\circ }} is not a constructible angle, since 9 = 33 {\displaystyle 9=3\cdot 3} is not the product of distinct Fermat primes as it contains 3 as a factor twice, and neither is π / 7 ≈ 25.714 ∘ ...

  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. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    Using the squeeze theorem, [4] we can prove that ⁡ =, which is a formal restatement of the approximation ⁡ for small values of θ. A more careful application of the squeeze theorem proves that lim θ → 0 tan ⁡ ( θ ) θ = 1 , {\displaystyle \lim _{\theta \to 0}{\frac {\tan(\theta )}{\theta }}=1,} from which we conclude that tan ⁡ ( θ ...

  7. A New Formula for Pi Is Here. And It’s Pushing Scientific ...

    www.aol.com/lifestyle/formula-pi-pushing...

    The digits of pi extend into infinity, and pi is itself an irrational number, meaning it can’t be truly represented by an integer fraction (the one we often learn in school, 22/7, is not very ...

  8. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The other four trigonometric functions (tan, cot, sec, csc) can be defined as quotients and reciprocals of sin and cos, except where zero occurs in the denominator. It can be proved, for real arguments, that these definitions coincide with elementary geometric definitions if the argument is regarded as an angle in radians. [ 5 ]

  9. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler . It is a special case of Euler's formula e i x = cos ⁡ x + i sin ⁡ x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } .