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Topic: Inverse trigonometric function

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	Trigonometric function - Wikipedia, the free encyclopedia
		The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin.
		The computation of trigonometric functions is a complicated subject, which can today be avoided by most people because of the widespread availability of computers and scientific calculators that provide built-in trigonometric functions for any angle.
		In this context the sine and cosine functions are used to describe one dimension projections of the uniform circular motion, the mass in a string movement, and a small angle approximation of the mass on a pendulum movement.
	en.wikipedia.org /wiki/Trigonometric_function (3946 words)

	Inverse function - Wikipedia, the free encyclopedia
		In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
		is also used for the (set valued) function associating to an element or a subset of the codomain, the inverse image of this subset (or element, seen as a singleton).
		Because the range of a left inverse is not restricted, we can adjoin to the domain of this injection an element "undefined", which we then assign to every element of the codomain which is not in the range.
	en.wikipedia.org /wiki/Inverse_function (844 words)

	Wikinfo \| Trigonometric function
		In mathematics, the trigonometric functions are functions of an angle important when studying triangles and modeling periodic phenomena.
		The trigonometric functions are not monotonic, so we must restrict their domains before we are able to define a unique inverse.
		The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 B.C.), who tabulated the lengths of circle arcs (equivalent to an angle A times radius r) with the corresponding chords (equivalent to 2r sin(A/2)).
	www.wikinfo.org /wiki.php?title=Trigonometric_function (1901 words)

	Trigonometric function
		In mathematics, the trigonometric functions are functionss of an angle, important when studying triangless and modeling periodic phenomena.
		A few other functions were common historically (and appeared in the earliest tables), but are now little-used, such as the versed sine (versin = 1 − cos) and the exsecant (exsec = sec − 1).
		The earliest systematic study of trigonometric functions and tabulation of their values was performed by Hipparchus of Nicaea (180-125 BC), who tabulated the lengths of circle arcs (angle A times radius r) with the lengths of the subtending chords (2r sin(A/2)).
	www.xasa.com /wiki/en/wikipedia/t/tr/trigonometric_function.html (2773 words)

	Trigonometric identity
		In mathematics, trigonometric identities are equations involving trigonometric functions that are true for all values of the occurring variables.
		An important application is the integration of non-trigonometric functions: a common trick involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
		If the trigonometric functions are defined in terms of geometry, then their derivatives can be found by verifying two limits.
	www.brainyencyclopedia.com /encyclopedia/t/tr/trigonometric_identity.html (1374 words)

	Inverse Trigonometric Functions
		Since the trigonometric functions are not one-to-one functions, they do not have inverse functions in the customary sense.
		The inverse trigonometric functions are found by inverting just the portion of the corresponding trigonometric function on the intervals specified above.
		In Exercises 4.5.6 and 4.5.7 you used the Right Triangle Method to find all the trigonometric functions of an angle A given the value of one of the trigonometric functions of A. The next exercises are the same type of problem in different clothing.
	jwbales.home.mindspring.com /precal/part4/part4.6.html (477 words)

	Inverse trigonometric function - Wikipedia, the free encyclopedia
		In mathematics, the inverse trigonometric functions are a set of relationships closely related to the trigonometric functions.
		These functions may also be defined by proving that they are integrals of other functions.
		These functions may also be expressed using natural logarithms.
	en.wikipedia.org /wiki/Inverse_trigonometric_function (236 words)

	SparkNotes: Trigonometric Equations: Terms and Formulae
		Inverse Trigonometric Relation - The relations arcsine, arccosine, arctangent, arccosecant, arcsecant, and arccotangent are the inverse of the trigonometric functions sine, cosine, tangent, cosecant, secant, and tangent, respectively.
		Inverse Trigonometric Function - An inverse relation in which the range is restricted such that there exists a one-to-one correspondence between inputs and outputs (numbers and angles, respectively).
		Inverse trigonometric functions are named exactly as inverse relations, except that the functions are capitalized.
	www.sparknotes.com /math/trigonometry/trigonometricequations/terms.html (250 words)

	LESSON #11 (Site not responding. Last check: 2007-10-08)
		The domain of a one-to-one (abbreviated 1-1) function is the range of the inverse function; the range of a 1-1 function is the domain of the inverse function.
		Sometimes you will hear people refer to the inverse of f instead of the inverse function of f: this is common practice and is technically referred to as abuse of language (in the first case inverse is a noun and in the second case inverse is an adjective).
		This is a typical example of the use of inverse functions: we may be familiar with the properties of a 1-1 function (in this case the derivative of the tangent function), but we need to know the 'equivalent' properties for the inverse function (in this case, the derivative of the inverse tangent function).
	www.hcc.hawaii.edu /distance/math140/lesson11.htm (2219 words)

	Math 1040 (Site not responding. Last check: 2007-10-08)
		1.1 - Evaluate the inverse trigonometric functions for a given number using the definitions or a scientific calculator as appropriate.
		(sin t) that are a composition of the sine, cosine or tangent and the associated inverse trigonometric function where x and t are specific numbers by using the definitions of the inverse trigonometric functions.
		x) that are a composition of the sine, cosine or tangent with an inverse trigonometric function where x is a specific number by using the definitions of the functions involved.
	www.colorado.edu /math/umap/OneCredit/Objectives/1040.html (436 words)

	Inverse Trigonometric Functions (Site not responding. Last check: 2007-10-08)
		This lesson studies the inverse of standard trigonometric functions by teaching you how to find angles that correspond to any given value.
		Unlike standard trigonometric functions where you find values of an angle, in the inverse trigonometric function, you are finding the angles of given values.
		All inverse trigonometric functions must have two values and all functions can be evaluated by use of radians and degrees.
	www.angelfire.com /magic2/snowtigerwave (66 words)

	Expressions - Geometry
		The inverse functions tell you which angle would produce the value you've specified with the corresponding trigonometric function.
		This is because the function is written to expect y to correspond to the opposite and x to the adjacent, making the tangent equal to y/x.
		Finally, we convert the output of this function from radians_to_degrees, and pass the results to whatever parameter we've assigned the expression to.
	www.jjgifford.com /expressions/geometry/inverse_functions.html (632 words)

	Manual for math - man math (Site not responding. Last check: 2007-10-08)
		Its properties are reflected fairly faithfully in the elementary functions for a VAX distributed in 4.3 BSD.
		Some of the VMS functions are a little faster, some are a little more accurate, some are more puritani- cal about exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), and most occupy much more memory than their counterparts in libm.
		But simulating all three characteristics of an atomic function is still a tedious affair, entailing hosts of tests and saves-restores; work is under way to ameliorate the inconvenience.
	tautology.org /software/man/math (2525 words)

	Trigonometric Functions - Inverse Trig. Functions and their Graphs (Site not responding. Last check: 2007-10-08)
		A function has an inverse function strictly when no horizontal line intersects the graph more than once.
		functions don't have inverse functions, and it is useful to have an inverse function, a restriction is applied to the domain so that an inverse function might exist.
		The range of the function with its restricted domain is the same as the range of the original function.
	library.thinkquest.org /10030/2inverse.htm (236 words)

	MTH 175 - Monroe Community College Web Site
		2.8 Determine the domain, range, intercepts, and intervals where the function is increasing or decreasing for polynomial functions, piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions.
		2.15 Graph piecewise functions, absolute value functions, rational functions, logarithmic functions, exponential functions, trigonometric functions, families of functions, and the composition of these functions manually and using the graphing calculator.
		4.20 Given the graph of a trigonometric function, determine the amplitude, period, phase shift and vertical shift.
	www.monroecc.edu /depts/math/mth175.htm (994 words)

	derivatives of hyperbolic functions (Site not responding. Last check: 2007-10-08)
		Table of derivatives for hyperbolic functions, i.e., sinh, cosh, tanh, coth, sech, and csch, and inverse hyperbolic functions, i.e., arcsinh, arccosh, arctanh, arccoth, arcsech, and arccsch.
		The hyperbolic functions are defined in terms of ex and e-x.
		Functions, Derivatives of Hyperbolic Functions, Derivatives of Inverse Hyperbolic Functions, Derivatives of...
	www.money-smash.com /articles/74/derivatives-of-hyperbolic-functions.html (663 words)

	Inverse Functions Tutorial
		However, for a function to have an inverse function, it must be one-to-one.
		Although trigonometric functions are not one-to-one, (try applying the horizontal line test to y = sin x, for example), we can restrict the domain so that they become one-to-one functions.
		The inverse cosine function is still correct, but it is preferred that you express the integral as the inverse sine function.
	www.nipissingu.ca /calculus/tutorials/inverse.html (1480 words)

	TRIGONOMETRY FOR STATICS-Part 1
		The trigonometric functions are named sine, cosine, tangent, cotangent, secant, and cosecant.
		The values of the trigonometric functions for this angle are given as:
		The same rule does not apply to negative exponents since the exponent "-1" is reserved for the inverse trigonometric function.
	em-ntserver.unl.edu /Math/mathweb/trigonom/trigsA97.html (264 words)

	Standards of Learning (Site not responding. Last check: 2007-10-08)
		MAT.TRG.1 The student will use the definitions of the six trigonometric functions to find the sine, cosine, tangent, cotangent, secant, and cosecant of an angle in standard position, given a point, other than the origin, on the terminal side of the angle.
		MAT.TRG.3 The student will find the values of the trigonometric functions of the special angles and their related angles as found in the unit circle without the aid of a calculating utility.
		The graphing calculator will be used to investigate the effect of changing A, B, C, and D on the graph of a trigonometric function.
	www.knowledge.state.va.us /main/sol/solview.cfm?curriculum_abb=MAT&category_abb=TRG (356 words)

	Inverse Function -- from Wolfram MathWorld
		However, inverse functions are commonly defined for elementary functions that are multivalued in the
		Inverse, Inverse Function Theorem, Inverse Hyperbolic Functions, Inverse Trigonometric Functions, Series Reversion.
		Jeffreys, H. and Jeffreys, B. "Inverse Functions." §1.066 in Methods of Mathematical Physics, 3rd ed.
	mathworld.wolfram.com /InverseFunction.html (213 words)

	Math Tools Browse (Site not responding. Last check: 2007-10-08)
		Discusson, with examples, of an application of the derivative of the inverse tangent to a predator-prey sensing situation in fish.
		A Geometer's Sketchpad document used to create an applet to investigate the relationships between the sine function, the inverse sine function, and their derivatives.
		Investigate the relationships between the sine function, the inverse sine function, and their derivatives.
	mathforum.org /mathtools/cell/c,15.9.10,ALL,ALL (296 words)

	SparkNotes: Trigonometric Functions: Terms and Formulae
		Inverse Trigonometric Function - The inverses of the six trigononometric functions with specific restricted ranges.
		Period - The repeating interval of a periodic function; the period of a function is a real number.
		Trigonometric Functions - Sine, cosine, tangent, cosecant, secant, and cotangent are the six trigonometric functions.
	www.sparknotes.com /math/precalc/trigonometricfunctions/terms.html (457 words)

	Inverse Trigonometric Functions -- from Wolfram MathWorld
		The inverse trigonometric functions are the inverse functions of the trigonometric functions, written
		Since the inverse trigonometric functions are multivalued, they require branch cuts in the complex plane.
		Different conventions are possible for the range of these functions for real arguments.
	mathworld.wolfram.com /InverseTrigonometricFunctions.html (302 words)

	Inverse (Site not responding. Last check: 2007-10-08)
		When the value of a trigonometric function of an angle is known, the size of the angle can be found.
		The inverse trigonometric function, also known as the arc function, defines the angle based on the value of the trigonometric function.
		To calculate the inverse function of cot, csc, and sec, the reciprocal key must be pressed first then the SIN, COS, or TAN key.
	www.tpub.com /doemathematics/mathematics76.htm (237 words)

	VINO 0.50 Manual - man3-3/math.3-3.txt
		Its properties are reflected fairly faithfully in the ele- mentary functions for a VAX distributed in 4.3 BSD.
		Some of the VMS functions are a little faster, some are a little more accurate, some are more puritanical about May 6, 1991 3 MATH(3) MATH(3) exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), and most occupy much more memory than their counterparts in libm.
		But simulating all three characteristics of an atomic function is still a tedious affair, entailing hosts of tests and saves-restores; work is under way to amelio- rate the inconvenience.
	www.eecs.harvard.edu /~vino/vino/release-0.50/man/man3-3/math.3-3.html (2538 words)

	functions
		The use of trigonometric functions arises from the early connection between mathematics and astronomy.
		Business Functions is a library of up to nearly 500 high-performance functions running under Microsoft Excel, for financial analysis, planning and appraisal.
		The Bob Charest 8 piece band is perfect for any function from corporate events to the most unforgettable wedding.
	www.jointctr.org /?Category=functions (448 words)

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