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  2. Proofs of trigonometric identities - Wikipedia

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

    The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles , see Trigonometric functions . Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine , or on the differential equation f ″ + f = 0 ...

  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. Pythagorean trigonometric identity - Wikipedia

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

    satisfying respectively y(0) = 0, y′(0) = 1 and y(0) = 1, y′(0) = 0. It follows from the theory of ordinary differential equations that the first solution, sine, has the second, cosine, as its derivative, and it follows from this that the derivative of cosine is the negative of the sine. The identity is equivalent to the assertion that the ...

  5. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...

  6. Man Who Stabbed His Father 50 Times Reportedly Tells ... - AOL

    www.aol.com/man-stabbed-father-50-times...

    Jeffrey Goedde, 41, handed himself into the Jefferson County Sheriff’s Office on Wednesday, Dec. 18, according to court documents seen by PEOPLE

  7. Tori Spelling Admits One of Her Five Kids Didn't Get Any ...

    www.aol.com/lifestyle/tori-spelling-admits-one...

    The 'Beverly Hills: 90210' star and ex Dean McDermott share five kids — Liam, Stella, Hattie, Finn and Beau

  8. Differentiation of trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Differentiation_of...

    We conclude that for 0 < θ < ⁠ 1 / 2 ⁠ π, the quantity sin(θ)/θ is always less than 1 and always greater than cos(θ). Thus, as θ gets closer to 0, sin(θ)/θ is "squeezed" between a ceiling at height 1 and a floor at height cos θ, which rises towards 1; hence sin(θ)/θ must tend to 1 as θ tends to 0 from the positive side:

  9. Washington Mystics hire Jamila Wideman as general manager ...

    www.aol.com/washington-mystics-hire-jamila...

    The Washington Mystics hired Jamila Wideman as the franchise's new general manager and Sydney Johnson as the team's coach on Monday. Wideman joins the Mystics after spending six years at the NBA ...