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  2. 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.

  3. 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 ...

  4. Pythagorean trigonometric identity - Wikipedia

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

    Point P has a positive y-coordinate, and sin θ = sin(π − θ) > 0. As θ increases from zero to the full circle θ = 2π, the sine and cosine change signs in the various quadrants to keep x and y with the correct signs. The figure shows how the sign of the sine function varies as the angle changes quadrant.

  5. 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.

  6. 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 ...

  7. Weinberg angle - Wikipedia

    en.wikipedia.org/wiki/Weinberg_angle

    The 2004 best estimate of sin 2 θ w, at ∆q = 91.2 GeV/c, in the MS scheme is 0.231 20 ± 0.000 15, which is an average over measurements made in different processes, at different detectors. Atomic parity violation experiments yield values for sin 2 θ w at smaller values of ∆ q , below 0.01 GeV/ c , but with much lower precision.

  8. 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°).

  9. Theta graph - Wikipedia

    en.wikipedia.org/wiki/Theta_graph

    Example cone of a -graph emanating from with orthogonal projection line -graphs are specified with a few parameters which determine their construction. The most obvious parameter is , which corresponds to the number of equal angle cones that partition the space around each vertex. In particular, for a vertex , a cone about can be imagined as two infinite rays emanating from it with angle ...