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  2. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the ...

  3. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The sine and the cosine functions, for example, are used to describe simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. The sine and cosine functions are one-dimensional projections of uniform circular motion.

  4. List of trigonometric identities - Wikipedia

    en.wikipedia.org/wiki/List_of_trigonometric...

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

  5. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    Thus for many purposes it suffices to drop the cubic and higher terms and approximate the sine and tangent of a small angle using the radian measure of the angle, ⁠ ⁡ ⁡ ⁠, and drop the quadratic term and approximate the cosine as ⁠ ⁡ ⁠.

  6. Versine - Wikipedia

    en.wikipedia.org/wiki/Versine

    On the other hand, the versed sine of θ is the distance CD from the center of the chord to the center of the arc. Thus, the sum of cos(θ) (equal to the length of line OC) and versin(θ) (equal to the length of line CD) is the radius OD (with length 1). Illustrated this way, the sine is vertical (rectus, literally "straight") while the versine ...

  7. Sinc function - Wikipedia

    en.wikipedia.org/wiki/Sinc_function

    The local maxima and minima of the unnormalized sinc correspond to its intersections with the cosine function. That is, ⁠ sin(ξ) / ξ ⁠ = cos(ξ) for all points ξ where the derivative of ⁠ sin(x) / x ⁠ is zero and thus a local extremum is reached.

  8. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    Fig. 1a – Sine and cosine of an angle θ defined using the unit circle Indication of the sign and amount of key angles according to rotation direction Trigonometric ratios can also be represented using the unit circle , which is the circle of radius 1 centered at the origin in the plane. [ 37 ]

  9. Hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Hyperbolic_functions

    The hyperbolic sine and the hyperbolic cosine are entire functions. As a result, the other hyperbolic functions are meromorphic in the whole complex plane. By Lindemann–Weierstrass theorem , the hyperbolic functions have a transcendental value for every non-zero algebraic value of the argument.