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The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then = , and the law of cosines reduces to = + . The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.
The Latin brocard nemo judex in causa sua has its origins in the Roman legal tradition and is codified within the Corpus Juris Civilis.In 376 AD, an imperial decree established the principle that "no one shall decide his own case or interpret the law for himself" (neminem sibi esse iudicem vel ius sibi dicere debere) (Code 3.5.1).
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 that is 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 ...
Herbert Broom′s text of 1858 on legal maxims lists the phrase under the heading ″Rules of logic″, stating: Reason is the soul of the law, and when the reason of any particular law ceases, so does the law itself. [9] ceteris paribus: with other things the same More commonly rendered in English as "All other things being equal."
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.
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°).
In English law, natural justice is technical terminology for the rule against bias (nemo iudex in causa sua) and the right to a fair hearing (audi alteram partem).While the term natural justice is often retained as a general concept, it has largely been replaced and extended by the general "duty to act fairly".
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: