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Topic: Inverse tangent

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	Arc Tangent - Search Results - MSN Encarta
		Arc Tangent, in trigonometry, the inverse of the tangent function.
		Tangent (trigonometry), one of the six fundamental ratios of trigonometry.
		An arc of a circle is often expressed in degrees and corresponds to the...
	encarta.msn.com /Arc_Tangent.html (151 words)

	Inverse Trig Functions
		(X) is known as the inverse sine function and it is NOT equal to 1/Sin(X).
		(X) is the known inverse tangent function and is NOT equal to 1/Tan(X).
		However, this function is not single valued, and since the tangent function is positive in the first and third quadrants, the other value would be 180° + 11.3° which is 191.3°.
	library.thinkquest.org /C0121962/inversefunctions.htm (240 words)

	MSN Encarta - Search Results - Tangent
		Tangent (geometry), a line, line segment, or ray that touches a circle at one and only one point.
		Tangent (trigonometry), one of the six fundamental ratios of trigonometry.
		Arc Tangent, in trigonometry, the inverse of the tangent function.
	ca.encarta.msn.com /Tangent.html (122 words)

	Projection of World Population
		A generalized version of the inverse tangent function is devised and found to yield an excellent fit to the World population data.
		The generalized inverse tangent function is even more realistic, because it allows for an asymmetry; and it yields overwhelmingly the best fit of the four functions to the World data.
		Since the generalized inverse tangent function yields such an excellent fit to the data and since its projection is excellent over the last decade, its projection into the future must be seriously considered.
	arts.bev.net /roperldavid/WorldPop.htm (3738 words)

	tangent - Search Results - MSN Encarta
		Tangent (geometry), a line, line segment, or ray that touches a circle at one and only one point.
		The line is said to be tangent to the circle or is...
		Tangent (trigonometry) : pictures and illustrated related to tangents
	encarta.msn.com /tangent.html (184 words)

	SparkNotes: Trigonometric Functions: Inverse Trigonometric Functions
		Thus, the range of the inverses of the trigonometric functions must be restricted to make them functions.
		The six inverse trigonometric functions are arcsine, arccosine, arctangent, arccosecant, arcsecant, and arccotangent.
		This symbolism for the inverse of the functions should not be confused with negative exponents.
	www.sparknotes.com /math/precalc/trigonometricfunctions/section4.rhtml (282 words)

	Inverse Trigonometric Functions
		Inverse trigonometric functions are explored interactively using an applet.
		Use the slider to move a marker (blue) along the graph of f(x) and another marker (red) along the graph of its inverse.
		Use the slider to move a marker (blue) along the graph of g(x) and another marker (red) along the graph of its inverse.
	www.analyzemath.com /Inverse-Trigonometric-Functions/Inverse-Trigonometric-Fun.html (775 words)

	CLHS: Function SINH, COSH, TANH, ASINH... (Site not responding. Last check: 2007-10-14)
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in the next figure.
		The branch cut for the inverse hyperbolic sine function is in two pieces: one along the positive imaginary axis above i (inclusive), continuous with quadrant I, and one along the negative imaginary axis below -i (inclusive), continuous with quadrant III.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -i/2 and i/2 excluded.
	www.lisp.org /HyperSpec/Body/fun_sinhcm_co_coshcm_atanh.html (460 words)

	Calculus I (Math 2413) - Derivatives - Derivatives of Inverse Trig Functions (Site not responding. Last check: 2007-10-14)
		In this section we are going to look at the derivatives of the inverse trig functions. In order to derive the derivatives of inverse trig functions we’ll need the formula from the last section relating the derivatives of inverse functions.
		Simplifying the denominator is similar to the inverse sine, but different enough to warrant showing the details. We’ll start with the definition of the inverse tangent.
		There are three more inverse trig functions but the three shown here the most common ones. Formulas for the remaining three could be derived by a similar process as we did those above. Here are the derivatives of all six inverse trig functions.
	tutorial.math.lamar.edu /AllBrowsers/2413/DiffInvTrigFcns.asp (729 words)

	Trigonemetric Inverse
		When you use a calculator to take the trigonometric inverse to find an angle, it returns just one value, the principle value.
		Which angle is the correct angle depends upon the details of the problem you are solving, i.e.
		Note that there are actually an infinite number of solutions of any trigonometric inverse if you do not limit you answers to be between 0 and 360 degrees.
	www.ac.wwu.edu /~vawter/PhysicsNet/Topics/Vectors/TrigInverse.html (182 words)

	Calcute functions: logarithm, inverse hyperbolic cotangent, arc-cosecant, hyperbolic inverse cosecant, arc-cotangent, ...
		Calcute functions: logarithm, inverse hyperbolic cotangent, arc-cosecant, hyperbolic inverse cosecant, arc-cotangent, inverse hyperbolic secant, arc-secant...
		Arc-tangent (arctangent, inverse tangent) value expressed using the currently-selected angle unit.
		Tangent of an angle in the currently-selected unit.
	calcute.com /functions.html (629 words)

	Inverse Functions, Part 3
		In Part 2 we constructed the inverse of the (restricted) sine function as a "function defined by an integral":
		The inverse sine function is, by definition, the inverse of the function defined by that equation (with the domain restriction already noted).
		The inverse of the tangent function (arctangent, denoted arctan x) satisfies the equation tan y = x, where x is the independent variable, and y is the dependent variable.
	www.math.duke.edu /education/ccp/materials/intcalc/inverse/inverse3.html (628 words)

	Mathwords: Inverse Tangent
		With inverse tangent, we select the angle on the right half of the unit circle having measure as close to zero as possible.
		Note: arctan refers to "arc tangent", or the radian measure of the arc on a circle corresponding to a given value of tangent.
		Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions.
	www.mathwords.com /t/tangent_inverse.htm (189 words)

	Derivatives of Inverse Trigonometric Functions
		It is possible to form inverse functions for restricted versions of all six basic trigonometric functions.
		However, it is generally enought to consider the inverse sine and the inverse tangent functions.
		We apply the chain rule to the left end, remembering that the derivative of the sine function is the cosine function and that y is a differentiable function of x.
	oregonstate.edu /instruct/mth251/cq/Stage6/Lesson/invTrigDeriv.html (731 words)

	fixatan(3): Fixed point inverse tangent lookup ... - Linux man page (Site not responding. Last check: 2007-10-14)
		This function finds the inverse tangent of a value using a lookup table.
		The inverse tangent is the value whose tangent is `x'.
		Returns the inverse tangent of a fixed point value, measured as a fixed point binary format angle.
	www.die.net /doc/linux/man/man3/fixatan.3.html (66 words)

	Inv2_Tang_Derivative.html
		The range of an inverse is the domain the original function.
		So the blue is f, red is the inverse, the lower green is f ', upper green is the derivative of the inverse, and the plums are the tangent lines.
		The negative parts the of derivative of the inverse are so far into the negative range that it would distort the plot too much if I tried to include them.
	www.adeptscience.co.uk /maplearticles/f1010.html (1867 words)

	ANSI and GNU Common Lisp Document - sinh
		These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument x as given in Figure 12--15.
		The branch cut for the inverse hyperbolic tangent function is in two pieces: one along the negative real axis to the left of -1 (inclusive), continuous with quadrant III, and one along the positive real axis to the right of~1 (inclusive), continuous with quadrant I. The points -1 and~1 are excluded from the domain.
		Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points -\pi i/2 and~\pi i/2 excluded.
	www.mathcs.duq.edu /simon/Gcl/gcl_767.html (523 words)

	T08-GraphsInverses.html
		An exploration of the graphs of the inverse sine, inverse cosine, and inverse tangent.
		The inverse tangent is the mirror image of the restricted sine.
		Notice that this variation of the tangent maps the real line into the open interval (0,1) as a one-to-one function - showing that there are same number of real numbers as there are real numbers in between 0 and 1.
	www.adeptscience.co.uk /products/mathsim/maple/powertools/trig/html/T08-GraphsInverses.html (501 words)

	CliffsNotes::Trigonometry Glossary (Site not responding. Last check: 2007-10-14)
		inverse cotangent function: defined in terms of the restricted tangent function.
		inverse notation: notation used to express an angle in terms of the value of trigonometric functions.
		inverse tangent function: inverse of the restricted tangent function.
	www.cliffsnotes.com /WileyCDA/Section/id-106382.html (616 words)

	Tangent ratio 2
		Note: The tangent ratio does have meaning for angles outside the range of 0º to 90º, but these angles do not apply to right angled triangles, and so will not be discussed here.
		Tangent ratios used to be printed in books of tables.
		Type the tangent ratio as a decimal fraction: eg 0.6, OR as a ratio of two sides, eg: 3/5.
	www.teacherschoice.com.au /Maths_Library/Trigonometry/tangent_ratio_2.htm (773 words)

	LESSON #11 (Site not responding. Last check: 2007-10-14)
		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)

	Common Trigonometry Mistakes Example: Value of inverse tangent (Site not responding. Last check: 2007-10-14)
		(x) means the inverse tangent of x, that is, the function that undoes the tangent function.
		The inverse trigonometric functions are most usefully defined with the range in radian measure.
		If degree measure is to be used, then the value of the inverse trigonometric function must clearly indicate that choice by giving (in this example) the answer as 45°.
	mathmistakes.info /mistakes/trig/Examples/8/ctm.html (211 words)

	MTH 185 Test 3 (Site not responding. Last check: 2007-10-14)
		The inverse function of sine provides as an output the angle which provides a certain value of sine.
		A calculator would say, inverse sine of (1/Ö2) is 45º, but we can see form the picture that the angle is obtuse and thus must be 90º + 45º = 135º.
		The inverse functions of cosine, tangent, secant, cosecant, and cotangent are defined similarly.
	users.stlcc.edu /amosher/April2.htm (240 words)

	Complex Number Inverse Trigonometric Functions
		The following complex number algorithms are the inverses of trigonometric functions currently present in the C++ standard.
		Effects: returns the inverse tangent of the complex number z.
		Effects: returns the inverse hyperbolic tangent of the complex number z.
	www.boost.org /regression-logs/cs-win32_metacomm/doc/html/boost_math/inverse_complex.html (295 words)

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