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Topic: Logarithmic tangent

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	tangent - definition from Biology-Online.org
		(Science: geometry) A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced.
		(Science: physics) Tangent galvanometer, a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current.
		Tangent of an arc, a right line, as ta, touching the arc of a circle at one extremity a, and terminated by a line ct, passing from the center through the other extremity o.
	www.biology-online.org /dictionary/tangent (224 words)

	Chapter Tamperer <i>to</i> Tant of T by Webster's Dictionary (1913 Edition)
		A tangent line curve, or surface; specifically, that portion of the straight line tangent to a curve that is between the point of tangency and a given line, the given line being, for example, the axis of abscissas, or a radius of a circle produced.
		a decimal expressing the length of the tangent of an arc, the radius being reckoned unity.
		a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current.
	www.bibliomania.com /2/3/257/1211/24279/3.html (377 words)

	FanFiction.Net : Dictionary & Thesaurus (Site not responding. Last check: 2007-11-03)
		Natural tangent, a decimal expressing the length of the tangent of an arc, the radius being reckoned unity.
		Tangent galvanometer (Elec.), a form of galvanometer having a circular coil and a short needle, in which the tangent of the angle of deflection of the needle is proportional to the strength of the current.
		Tangent of an angle, the natural tangent of the arc subtending or measuring the angle.
	www.fanfiction.net /dictionary.php?word=Tangent (329 words)

	FUNCTION - Online Information article about FUNCTION
		T The tangent PT at P is regarded as identical with the secant PQ, and the position of the tangent is determined by the similarity of the triangles PTM, PQR.
		In connexion with the problem of maxima and minima, it is noted that the differential of y is positive or negative according as y increases or decreases when x increases, and the discrimination of maxima from minima depends upon the sign of ddy, the differential of dy.
		A tangent is defined as a line joining two " infinitely " near points of a curve, and the " infinitely " small distances (e.g., the distance between the feet of the ordinates of such points) are said to be expressible by means of the differentials (e.g., dx).
	encyclopedia.jrank.org /FRA_GAE/FUNCTION.html (8019 words)

	Cams
		The logarithmic spiral is a mathematical curve which has the unique property of maintaining a constant angle between the radius and the tangent to the curve at any point on the curve (figure 1).
		A logarithmic spiral cam (a "constant angle cam") ensures that the line between the axle and the point of contact (the "line of force") is at a constant angle to the abutting surface, independent of how the cam is oriented.
		The mathematical equation for a logarithmic spiral is R=beaØ.
	www.bigwalls.net /climb/camf (1137 words)

	logarithmic spiral
		The angle any tangent to the curve makes with a tangent to a circle at the same radius, known as the pitch angle, is constant and results in a logarithmic spiral being self-similar: in other words, any part of it looks like any other part (though possibly rotated).
		Hawks approach their prey in the form of a logarithmic spiral and their sharpest view is at an angle to their flight direction that is the same as the spiral's pitch.
		The logarithmic spiral was first described by René Descartes and later studied in depth by Jakob Bernoulli, who called it Spiralis mirabilis (the Wonderful Spiral) and wanted one engraved on his tombstone.
	www.daviddarling.info /encyclopedia/L/logarithmic_spiral.html (432 words)

	Math 160 Objectives
		Be able to relate tangent lines to the limit of secant lines.
		Be able to graph any type of function (to include rational, trigonometric, logarithmic, and exponential functions) and display them in the most appropriate window.
		Know the values of sine, cosine, and tangent for the angles 0, pi/6, pi/4, pi/3, and pi/2 and their analogs in the other 3 quadrants.
	www.math.colostate.edu /~calc/m160/Objectives.htm (530 words)

	MK IV.A Detail
		From the illustration in Plate VIII it will be seen that there is a logarithmic scale, three times repeated and thus covering a range from one to 103, on both the upper and lower edges of the slide.
		The upper part of the stock carries two pairs of sine and cosine scales, one pair extending from 0.5 ° to 90° and the other from 10° to 90°; the degrees from 0° to 20° on each cosine scale are marked on a small arc instead of being crowded together as in an ordinary slide-rule.
		A logarithmic scale, twice repeated, and identical with part of the slider scales, is also provided on the upper part of the stock; this permits of the rule being used in a limited way as an ordinary slide-rule.
	www.csulb.edu /~mbrenner/slide1.htm (729 words)

	HARCOURT MATHEMATICS 12 -- Advanced Functions and Introductory Calculus -- Web Links (Site not responding. Last check: 2007-11-03)
		This is the motion-picture version of the secant lines approach the tangent to a curve, so that the slope of the tangent line is the limit of the slopes of the secant lines.
		This shows the tangent line to a point on a curve, varying as the point moves along the curve.
		An animation illustrating a tangent to a function as it passes through a point at which the function is not differentiable.
	www.harcourtcanada.com /school/math/calculus/links.htm (2018 words)

	Notes on the Logarithmic Spiral
		In the second proposition Newton showed that the logarithmic spiral would also be described by a particle attracted to the pole by a force proportional to the square of the density of the medium in which it moves, while this density is at each point inversely proportional to its distance from the pole.
		The logarithmic spiral is its own polar reciprocal with respect to any equilateral hyperbola which has its center at the pole and is tangent to the spiral.
		That the logarithmic spiral is a projection of a certain "elliptic logarithmic spiral" was shown in W. Hamilton, Elements of Quaternions, London, 1866, pp.
	www.spirasolaris.ca /rcarchibald.html (7069 words)

	Logarithmic function
		We define the logarithmic function as the inverse of the exponential function; hence, the derivative of the logarithmic function is d ln(x) / dx = 1 / x.
		That means that the limit of the logarithmic function, as x approaches zero, depends upon the angular direction of the approach.
		where this inverse tangent is to be taken in the semi-closed interval (- pi, pi], such that if a is the abscissa and b is the ordinate (in a Cartesian coordinate system), they determine the quadrant of the inverse tangent.
	www.rism.com /Trig/logarith.htm (1456 words)

	logarithmic spiral
		The logarithmic relation between radius and angle leads to the name of logarithmic spiral or logistique (in French).
		The logarithmic spiral is the curve for which the angle between the tangent and the radius (the polar tangent) is a constant.
		Johan Gielis extended the logarithmic spiral to a super spiral.
	www.2dcurves.com /spiral/spirallo.html (651 words)

	Course 4 Unit 3 - Logarithmic Functions and Data Models
		Unit 3, Logarithmic Functions and Data Models, develops student understanding of logarithmic functions and their use in modeling and analyzing problem situations and data patterns.
		Students will develop an understanding of inverse functions, the operation of composing functions, and logarithmic scales in the process of meeting the objectives of the unit.
		The properties of logarithms are developed and used to rewrite expressions and solve equations involving logarithmic expressions.
	www.wmich.edu /cpmp/unitsamples/c4u3/c4u3intro.html (544 words)

	[No title]
		Graph power functions with integer powers, root functions, exponential and logarithmic functions, the absolute value function, the greatest integer function, trigonometric functions (sine, cosine, and tangent), and inverse trigonometric functions (arcsine, arccosine, and arctangent) b.
		Describe the behavior of functions using domain, range, intervals of increase and decrease, intervals where the graph of the function is above the x-axis or below the x-axis, even or odd definitions, and one-to-one properties e.
		Identify and graph the following types of equations in two variables: linear, absolute value, exponential, logarithmic, split-domain, square root, polynomial in factored form, rational, trigonometric, and equations in two unknowns whose graphs are parabolas or circles 8.
	www.gpc.edu /~mcse/CourseDocs/CcoTg_F1998_S2000/ccom130 (1109 words)

	Finding an Equation of a Line Tangent to a point on a Graph
		The tangent line is related to differentiating an equation.
		Differentiating an equation yields an equation that is useful in finding the slope of a line tangent to the graph of the equation, in which we differentiated, for any value of x.
		Note: If f(x) is a function, f’(x) will give us a function that is useful in finding the slope of a line tangent to f(x) that passes through any value of x.
	students.uww.edu /muellerbt15/tan.htm (494 words)

	[No title]
		Quiz on determining which graph is the graph of a function, its derivative and its 2nd derivatives.
		Drill on finding the derivative and the equation of the tangent line at a given point.
		Drill on finding the derivative and the tangent line to the inverse of a function.
	archives.math.utk.edu /visual.calculus/3 (575 words)

	Soviet Calculators History
		Simultaneously with the abacuses, still during the pre-revolutionary years (1917), the logarithmic (slide) rulers were used in scientific circles, practically without change, since the XVII century.
		The logarithmic slide rule was no longer necessary, and the margin of error was no longer a concern.
		However, an error was detected on the first series of these calculators: when adding a number containing seven nines in the mantissa and a nine in the eighth digit, which is not displayed - to a number larger than four, an error occurs.
	www.xnumber.com /xnumber/russian_calcs.htm (7136 words)

	ipedia.com: Slide rule Article (Site not responding. Last check: 2007-11-03)
		A logarithm transforms an operation of multiplication or division to one of addition or subtraction to the rules log (a·b) = log a + log b and log (a/b) = log a - log b.
		By the use of the logarithmic transform multiplication and division can be carried out.
		The most popular were trigonometric, usually sine and tangent, logarithm of logarithm (base 10) (for taking the log of a value on a multiplier scale), natural logarithm and exponential scales.
	www.ipedia.com /slide_rule_1.html (1529 words)

	Logarithmic and Trigonometric Calculator Home Page
		This calculator will calculate logarithms, trigonometric functions, and the logarithms of trigonometric functions.
		To calculate the logarithm of the value, check the logarithm box.
		To calculate the logarithm of a trigonometric function applied to the value, check the logarithm box and choose a trigonometric function.
	pollux.nss.nima.mil /calc/trig.html (76 words)

	index.html
		The logarithm of a product produces the inverse of the product times the product rule
		Where is tangent horizontal - or where is the derivative = 0
		An equation of the tangent that passes through (0, 0)
	www.richmond.edu /~lwibberl/math211/review3 (379 words)

	The Geometry Junkyard: All Topics
		Circle fractal based on repeated placement of two equal tangent circles within each circle of the figure.
		This shape, constructed by inscribing circular arcs in a spiral tiling of squares, resembles but is not quite the same as a logarithmic spiral.
		Thomas Banchoff relates these two results, on colinearity of intersections of external tangents to disjoint circles, and of intersections of sides of perspective triangles, respectively.
	www.ics.uci.edu /~eppstein/junkyard/all.html (9742 words)

	Citebase - On Varieties with trivial logarithmic tangent bundle (Site not responding. Last check: 2007-11-03)
		We characterize Kaehler manifolds with trivial logarithmic tangent bundle (with respect to a divisor D) as a class of certain compatifications of complex semi-tori.
		Use the Correlation Generator to explore the correlation between download impact ("hits") and citation impact.
		ON MANIFOLDS WITH TRIVIAL LOGARITHMIC TANGENT BUNDLE 11 [3] A. Borel:Compact Clifford Klein forms of symmetric spaces, Topology 2 (1963), 111-122.
	www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0210263 (341 words)

	IB Math Methods 2 - Assignment Schedule
		Day 1: Worksheet "1.1 Introduction to the Calculus - Tangent Lines and Limits." Read § 1.1 … NB … nota bena (note well!) … that you are expected to read every section we cover.
		In this case, you are deriving the derivative of the trig functions.
		121-122, # 51 (use "Draw, Tangent" features of TI-83) plus include a "careful" sketch, # 57 (include a "careful" sketch of the graph with horizontal tangent lines), # 59 - 64 (all), and 67.
	users.rcn.com /mwhitney.massed/ibmm2-pacing.html (1787 words)

	SOLVING TRIGONOMETRIC EQUATIONS
		If you would like an in-depth review of logarithms, the rules of logarithms, logarithmic functions and logarithmic equations, click on logarithmic functions.
		To solve for x, first isolate the tangent term.
		If we restrict the domain of the tangent function to
	www.sosmath.com /algebra/solve/solve9/s91/s9111/s911103/s911103.html (229 words)

	Detailed Course Syllabus (Site not responding. Last check: 2007-11-03)
		0.3 exponential, logarithmic, and trigonometric functions; transformations of functions
		2.3 derivatives of exponential, logarithmic, and trigonometric functions
		3.9 sketch the graphs of certain exponential, logarithmic and trigonometric functions
	www.ccaurora.edu /mat201/syllabus.htm (725 words)

	ST
		Topics include limits and continuity, the derivative with applications to tangent lines, rectilinear motion, related rates, mean value theorem, curve sketching, and optimization; antiderivatives, area, and the definite integrals; and derivatives and integrals involving logarithmic and exponential functions.
		Evaluate definite integrals using Riemann sums and the Fundamental Theorem of Calculus
		Solve problems involving tangent lines, area, curve sketching, rates of change, optimization, rectilinear motion, related rates, exponential growth and decay
	www.sjrcc.cc.fl.us /facultyinfo/mac2311.html (308 words)

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