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If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable. [3] A variation on the law of cosines, the second spherical law of cosines, [4] (also called the cosine rule for angles [1]) states:
Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c.. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles.
In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I 0 cos θ.
For example, Todhunter [1] gives two proofs of the cosine rule (Articles 37 and 60) and two proofs of the sine rule (Articles 40 and 42). The page on Spherical law of cosines gives four different proofs of the cosine rule. Text books on geodesy [2] and spherical astronomy [3] give different proofs and the online resources of MathWorld provide ...
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 ...
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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.
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