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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. 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 ...

  4. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    Half-angle and angle-addition formulas [ edit ] Historically, the earliest method by which trigonometric tables were computed, and probably the most common until the advent of computers, was to repeatedly apply the half-angle and angle-addition trigonometric identities starting from a known value (such as sin(π/2) = 1, cos(π/2) = 0).

  5. Pythagorean trigonometric identity - Wikipedia

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

    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 involving the cotangent and the cosecant also follows from the Pythagorean theorem.

  6. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The red section on the right, d, is the difference between the lengths of the hypotenuse, H, and the adjacent side, A.As is shown, H and A are almost the same length, meaning cos θ is close to 1 and ⁠ θ 2 / 2 ⁠ helps trim the red away.

  7. NYT ‘Connections’ Hints and Answers Today, Friday, December 13

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    Today's NYT Connections puzzle for Friday, December 13, 2024The New York Times. ... 2. These are used to sort/organize digital messages. 3. Fizzy beverages with a sharp, zesty taste. 4. The words ...

  8. NYT ‘Connections’ Hints and Answers Today, Sunday, December 15

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    Today's NYT Connections puzzle for Sunday, December 15, 2024The New York Times. ... The very best gifts for men, from $2 to over $100. AOL. These glass food containers are over 40% off: 'I like ...

  9. Sugar Bowl: No. 2 Georgia vs. Notre Dame/Indiana winner, 8:45 p.m. (ESPN) When are College Football Playoff semifinals? The semifinal games will be played Jan. 9 and Jan. 10 at the site of two ...