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  2. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The trigonometric functions of angles that are multiples of 15°, 18°, or 22.5° have simple algebraic values. These values are listed in the following table for angles from 0° to 45°. [1] In the table below, the label "Undefined" represents a ratio :

  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. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    The values for a/b·2π can be found by applying de Moivre's identity for n = a to a b th root of unity, which is also a root of the polynomial x b - 1 in the complex plane. For example, the cosine and sine of 2π ⋅ 5/37 are the real and imaginary parts , respectively, of the 5th power of the 37th root of unity cos(2π/37) + sin(2π/37)i ...

  5. Pythagorean trigonometric identity - Wikipedia

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

    In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. 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 ...

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  7. 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.

  8. US judge issues order to reopen Citgo data room, restart bidding

    www.aol.com/news/us-judge-issues-order-reopen...

    A U.S. judge overseeing an auction of shares in the parent of Venezuela-owned Citgo Petroleum on Monday agreed to reopen a data room to allow potential buyers to prepare new bids, a court document ...

  9. Passengers experienced ‘hard jolt,’ then ‘free fall’ on ...

    www.aol.com/passengers-experienced-hard-jolt...

    A Hawaiian Airlines flight approaches Ellison Onizuka Kona International Airport at Keahole on the island of Hawaii on January 18, 2024. A 2022 incident of turbulence aboard a Hawaiian Airlines ...

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