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Quaternions and spherical trigonometry
Hamilton’s quaternion number system $latex {\mathbb{H}}&fg=000000$ is a non-commutative extension of the complex numbers, consisting of numbers of the form $latex {t + xi + yj + zk}&f…
Thus one can view(4) as a “master equation” for spherical trigonometry: in principle, it can be used to derive all the other laws of this subject. One can manipulate this constraint in various ways to obtain various trigonometric identities involving some subsets of these six parameters. Example 3 One application of Napier’s rule(6) is to determine the sunrise equation for when the sun rises and sets at a given location on the Earth, and a given time of year.
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