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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...

    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 trigonometric functions of θ are, for angles smaller than the right angle:

  4. Liu Hui's π algorithm - Wikipedia

    en.wikipedia.org/wiki/Liu_Hui's_π_algorithm

    The area within a circle is equal to the radius multiplied by half the circumference, or A = r x C /2 = r x r x π.. Liu Hui argued: "Multiply one side of a hexagon by the radius (of its circumcircle), then multiply this by three, to yield the area of a dodecagon; if we cut a hexagon into a dodecagon, multiply its side by its radius, then again multiply by six, we get the area of a 24-gon; the ...

  5. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    When radians (rad) are employed, the angle is given as the length of the arc of the unit circle subtended by it: the angle that subtends an arc of length 1 on the unit circle is 1 rad (≈ 57.3°), and a complete turn (360°) is an angle of 2 π (≈ 6.28) rad. For real number x, the notation sin x, cos x, etc. refers to the value of the ...

  6. Machin-like formula - Wikipedia

    en.wikipedia.org/wiki/Machin-like_formula

    The angle associated with a complex number (+) is given by: ⁡ Thus, in equation 4, the angle associated with the product is: ⁡ + Note that this is the same expression as occurs in equation 3.

  7. Euler's identity - Wikipedia

    en.wikipedia.org/wiki/Euler's_identity

    Additionally, when any complex number z is multiplied by , it has the effect of rotating counterclockwise by an angle of on the complex plane. Since multiplication by −1 reflects a point across the origin, Euler's identity can be interpreted as saying that rotating any point π {\displaystyle \pi } radians around the origin has the same ...

  8. List of formulae involving π - Wikipedia

    en.wikipedia.org/wiki/List_of_formulae_involving_π

    Sum S of internal angles of a regular convex polygon with n sides: S = ( n − 2 ) π {\displaystyle S=(n-2)\pi } Area A of a regular convex polygon with n sides and side length s :

  9. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    In astronomy, the angular size or angle subtended by the image of a distant object is often only a few arcseconds (denoted by the symbol ″), so it is well suited to the small angle approximation. [6] The linear size (D) is related to the angular size (X) and the distance from the observer (d) by the simple formula:

  1. Related searches 6 multiplied by pi 4 x right angle plus

    6 multiplied by pi 4 x right angle plus 2pi/4 value
    pi/4 calcpi/6
    pi equals 4