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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. Trigonometric functions of matrices - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions_of...

    The analog of the Pythagorean trigonometric identity holds: [2] ⁡ + ⁡ = If X is a diagonal matrix, sin X and cos X are also diagonal matrices with (sin X) nn = sin(X nn) and (cos X) nn = cos(X nn), that is, they can be calculated by simply taking the sines or cosines of the matrices's diagonal components.

  4. Proofs of trigonometric identities - Wikipedia

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

    There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles and the ratio between their sides.

  5. Pythagorean trigonometric identity - Wikipedia

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

    Alternatively, the identities found at Trigonometric symmetry, shifts, and periodicity may be employed. By the periodicity identities we can say if the formula is true for −π < θ ≤ π then it is true for all real θ. Next we prove the identity in the range π/2 < θ ≤ π, to do this we let t = θ − π/2, t will now be in the range 0 ...

  6. cis (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Cis_(mathematics)

    cis is a mathematical notation defined by cis x = cos x + i sin x, [nb 1] where cos is the cosine function, i is the imaginary unit and sin is the sine function. x is the argument of the complex number (angle between line to point and x-axis in polar form).

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  8. 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 ⁡ =, from which we conclude that ⁡ for small values of θ.

  9. Your Call: Go for 1 or 2 after a miracle late touchdown? - AOL

    www.aol.com/sports/call-1-2-miracle-touchdown...

    The decision. Washington head coach Dan Quinn opted to go for the extra point … and Seibert is now 22 of 24 on extra points. The kick again went wide left.

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