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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, 07:32 -0800

Ooops, sorry, should have added that detail. 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 > >