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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Need formulas for arcsin and arctan**

**From:**Lu Abel

**Date:**2006 Mar 28, 09:30 -0800

Whoops, in first paragraph should have said "You get radians by MULTIPLYING the angle in degrees by 2*Pi/360. Lu > We are most familiar with measuring angles in degrees. Mathematicians > like to measure them in radians which is a more "natural" unit (for > example, the formulae for calculating sines and cosines require an angle > to be measured in radians). There are 2*Pi radians going all the way > around a circle, just as there are 360 degrees. You get radians by > dividing the angle in degrees by 2*Pi/360. Your scientific calculator > will offer the option of expressing angles in either radians or degrees. > > On the other hand, regardless of whether an angle is expressed as 45 > degrees or Pi/4 radians, its sine and cosine are the same. So scanning > down a table that expresses angles in degrees for a sine or cosine that > matches your calculation should give you arcsine(x) in degrees. > > Lu Abel > > Bill wrote: > >>> Finally, since arcsine(x) is simply "the angle whose sine is x" scanning >>> down a conventional table of sines will easily give you the answer to a >>> degree... >> >> >> >> Exposing my ignorance (again), arcsine is a bit confusing to me. Every >> definition I find in my (old) reference books relates it to an angle in >> radians. >> >> As an analogy, "font" had a specific meeting prior to the computer. It >> meant not only a font "family" bit a specific size, weight, slant, >> compressions or expansion, designer or foundry etc.. 12 pt Caslon No. >> 540 >> Italic was one font, 14 pt Caslon No. 540 Italic another font, as was 36 >> point Bodoni Campanile (Ludlow). Now "font" is a very loose description, >> tied mostly to the intellectual-property laws. >> >> So my question, is/was "arcsine" a term that applied only to "the angle >> whose sine is x," in radians, while sin^-1 can apply to whatever system >> (degrees, rads, grads) one is working in? >> >> Thanks >> >> Bill >> >> > >