124.190.82.235: /* Equations */

2015-01-01T11:28:52Z

Equations

← Older revision		Revision as of 13:28, 1 January 2015
Line 1:		Line 1:
	~~[[Image:Exsecant~~ and ~~exosecant plot~~.~~png\|frame\|right\|exsecant (blue)~~ and ~~excosecant (green)]]~~		I am Oscar and I completely dig that name. Body developing is what my family and I appreciate. For many years he's been living in North Dakota and his family members enjoys it. Hiring is her day job now but she's usually needed her own business.<br><br>Look into my web site std home test ([http://www.pornteub.com/blog/32607 original site])
	~~[[Image:Circle-trig6~~.~~svg\|right\|thumb\|320px\|The trigonometric functions, including the exsecant, can be constructed geometrically in terms of a unit circle centered at~~ '~~'O''. The exsecant is the portion ''DE'' of the secant ''exterior'' to (''ex'') the circle.]]~~
	~~The '''exsecant''', also abbreviated '''exsec''', is a [[trigonometric function]] defined~~ in ~~terms of the secant function sec(θ):~~

	~~:<math>\operatorname{exsec}(\theta) = \sec(\theta) - 1~~. ~~\,</math>~~

	~~Once important in fields such as [[surveying]], [[astronomy]], and [[spherical trigonometry]], the exsecant function~~ is now ~~little-used. Mainly, this is because the availability of [[calculator]]s and [[computer]]s has removed the need for trigonometric tables of specialized functions such as this one.~~

	~~A related function is the '~~'~~'excosecant''' ('''excsc'''), the exsecant of the complementary angle:~~

	~~:<math>\operatorname{excsc}(\theta) = \operatorname{exsec}(\pi/2 - \theta) = \csc(\theta) - 1. \!</math>~~

	~~The reason to define a special function for the exsecant is similar to the rationale for the [[versine]]: for small [[angle]]~~s <var>θ</var>, the sec(<var>θ</var>) function approaches [[1 (number)\|one]], and so using the above formula for the exsecant will involve the [[subtraction]] of two nearly equal quantities and exacerbate roundoff errors. Thus, a table of the secant function would need a very high accuracy to be used for the exsecant, making a specialized exsecant table useful. ~~Even with a computer, [[floating point]] errors can be problematic for exsecants of small angles. A more accurate formula in this limit would be to use the identity:~~

	:<~~math~~>~~\operatorname{exsec}(\theta) = \frac{1-\cos(\theta)}{\cos(\theta)}~~
	~~= \frac{\operatorname{versin}(\theta)}{\cos(\theta)}~~
	~~= 2 \sin^2(\theta/2) \sec(\theta).\~~ <~~/math~~>

	~~Prior to the availability of computers, this would require time-consuming multiplications.~~

	~~The name ''exsecant'' can be understood from a graphical construction, at right, of the various trigonometric functions from a [[unit circle]], such as was used historically. sec~~(<var>θ</var>) is the [[secant line\|secant]] <math>\overline{OE}</math>, and the exsecant is the portion <math>\overline{DE}</math> of this secant that lies ''exterior'' to the circle (''ex'' is [[Latin]] for ''out of'').

	~~==See also==~~
	* [[List of trigonometric identities#Historic shorthands\|Trigonometric identities]]
	* [[Versine\|Versine and haversine]]

	~~==References==~~
	* M. Abramowitz and I. A. Stegun, eds., ''Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables'' (Dover: New York, 1972), p. 78. (See [[Abramowitz and Stegun]].)
	* James B. Calvert, [http://www.du.~~edu~~/~~~jcalvert~~/~~math/trig.htm Trigonometry~~] ~~(2004~~)~~. Retrieved 25 December 2004.~~

	~~[[Category:Trigonometry]]~~
	~~[[Category:Elementary special functions]]~~


	~~{{geometry-stub}}~~

en>Rjwilmsi: /* Examples */Journal cites, added 1 PMC using AWB (9513)

2013-10-19T16:57:23Z

Examples: Journal cites, added 1 PMC using AWB (9513)

Show changes

2.123.30.93: "is a pharmacological is a theoretical" = "is a pharmacological, theoretical"

2012-07-01T22:39:39Z

"is a pharmacological is a theoretical" = "is a pharmacological, theoretical"

Show changes

Volume of distribution - Revision history

124.190.82.235: /* Equations */

en>Rjwilmsi: /* Examples */Journal cites, added 1 PMC using AWB (9513)

2.123.30.93: "is a pharmacological is a theoretical" = "is a pharmacological, theoretical"