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Topic: Trigonometric sine function

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function mathematics

functional analysis

functional programming

trigonometric function

functional group

exponential function

probability density function

continuous functions

graph of a function

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function domain

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	SparkNotes: Trigonometric Functions: Reference Angles
		A periodic function is a function whose values (outputs) repeat in regular intervals.
		When we graph the trigonometric functions, we'll see that the period of sine, cosine, cosecant, and secant are 2π, and the period of tangent and cotangent is π.
		Due to the periodic nature of the trigonometric functions, the value of a trigonometric function at a given angle is always the same as its value at that angle's reference angle, except when there is a variation in sign.
	www.sparknotes.com /math/trigonometry/trigonometricfunctions/section4.rhtml (631 words)

	Trigonometric function
		The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.
		The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin.
		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.brainyencyclopedia.com /encyclopedia/t/tr/trigonometric_function.html (2545 words)

	Encyclopedia: Trigonometric function
		Both the sine and cosine functions satisfy the differential equation In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables.
		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.
		The trigonometric functions, as the name suggests, are of crucial importance in trigonometry, mainly because of the following two results: Trigonometry (from the Greek trigonon = three angles and metro = measure) is a branch of mathematics dealing with angles, triangles and trigonometric functions such as sine, cosine and tangent.
	www.nationmaster.com /encyclopedia/Trigonometric-function (5867 words)

	Learn more about Trigonometric function in the online encyclopedia. (Site not responding. Last check: 2007-09-10)
		The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
		The differentiability and continuity is then easily established, as is Euler's formula relating the trigonometric functions to the exponential function as well as the most remarkable formula in the world.
		The common number sin(A)/a occurring in the theorem is the reciprocal of the diameter of the circle through the three points A, B and C. The law of sines is useful for computing the lengths of the unknown sides in a triangle if two angles and one side are known.
	www.onlineencyclopedia.org /t/tr/trigonometric_function.html (1416 words)

	Trigonometry Tutorials and Problems
		The tangent function f(x) = a*tan(bx+c)+d and its properties such as graph, period, phase shift and asymptotes by changing the parameters a, b, c and d are explored interactively using an applet.
		The graph of the inverse trigonometric function arctan and its properties are explored using an applet.
		The graph and the properties of the inverse trigonometric function arcsin are explored using an applet.
	www.analyzemath.com /Trigonometry.html (792 words)

	The Six Trigonometric Functions
		The two basic trigonometric functions are: sine (which we have already studied), and cosine.
		The graph, as you might expect, is almost identical to that of the sine function, except for a "phase shift" (see the figure).
		The cosine curve is obtained from the sine curve by shifting it to the left a distance of
	people.hofstra.edu /faculty/Stefan_Waner/trig/trig2.html (898 words)

	Sine Function
		Explore interactively the sum of a sine and a cosine functionsSum of Sine and Cosine Functions
		Tutorial on the relationship between the amplitude, the vertical shift and the maximum and minimum of the sine functionTutorial on Sine Functions (2)- Problems
		Explore interactively the relationship between the graph of sine function and the coordinates of a point on the unit circle Unit Circle and Trigonometric Functions sin(x), cos(x), tan(x)
	www.analyzemath.com /trigonometry/sine.htm (437 words)

	Articles - Trigonometric function (Site not responding. Last check: 2007-09-10)
		All triangles are taken to exist in the Euclidean plane so that the inside angles of each triangle sum to Ï radians (or 180Â°).
		It can be shown from the series definitions that the sine and cosine functions are the imaginary and real parts, respectively, of the complex exponential function when its argument is purely imaginary:
		The values of sine, cosine and tangent of an angle of Ï/4 radians (45 degrees) can then be found using the Pythagorean theorem:
	www.wholez.com /articles/Sine (3110 words)

	Implementing the Sine function on the PIC
		For many applications it is necessary to use some basic trigonometry such as the sine function.
		On a small PIC it is impractical to use traditional methods such as series approximation or CORDIC to compute the sine function, so a table lookup is preferred.
		Because of the deeper return stack it is OK to call the four quadrant sine function from a subroutine.
	www.brouhaha.com /~eric/pic/sine.html (628 words)

	Earth Math
		This applet has two functions: First, it can be used to plot user supplied data.
		It can also be used to test if a user supplied trigonometric (sine) function (a function of the form y = a + b sin(k (x - c))) fits the given data by plotting the function.
		TRY will plot the trigonometric function corresponding to the coefficients supplied by the user.
	earthmath.kennesaw.edu /main_site/tool_chest/fitting_sine.htm (231 words)

	Sine - Trigonometric function - Wikipedia, the free encyclopedia
		Applet to explore the graph of sine function and its properties such as amplitude, period, phase shift through tutorials.
		The lesson make use of the dynamic graphing function which enables the student to discover the relationship of constants on the sine function.
		This "height" of a point on a unit circle is known as the sine of the angle determined by that point (from the center of the circle).
	esfind.com /esfd/sine.html (1076 words)

	The Side Angle Side Formula to Find A Triangle's Area. Sine to the rescue!
		The Side Angle Side formula for finding the area of a triangle is a way to use the sine trigonometric function to calculate the height of a triangle and use that value to find the area of the triangle.
		The Side Angle Side formula simply is an application of the sine function to find the height.
		The SAS formula is simply an application of sine to find the height of a triangle and then to use that height to find the triangle's area.
	www.mathwarehouse.com /trigonometry/area/side-angle-side-triangle.html (394 words)

	Application Notes - Details (Site not responding. Last check: 2007-09-10)
		The techniques and methods of approximation pre-sented here attempt to balance the usually conflicting goals of execution speed verses memory consumption, while still achieving full machine precision estimates.
		Although 32-bit arithmetic routines are available and constitute extended precision for the 24-bit versions, no extended precision routines are currently supported for use in the 32-bit routines, thereby requiring more sophisticated error control algorithms for full or nearly full machine precision function estimation.
		Differences in algorithms used for the PIC16CXXX and PIC17CXXX families are a result of performance and memory considerations and reflect the significant platform dependence in algorithm design.
	microchip.com /stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1824&appnote=en010982 (98 words)

	Modeling with the Sine Function
		Imagine a bicycle, wheel whose radius is one unit, with a marker attached to the rim of the rear wheel, as shown in the following figure.
		The function h(t) we get in the above way is called the sine function, denoted by sin(t).
		The sine of a real number t is given by the y-coordinate (height) of the point P in the following diagram, in which t is the distance of the arc shown.
	people.hofstra.edu /Stefan_Waner/trig/trig1.html (1118 words)

	COMAR VDT TIS
		non-sinusoidal: A waveform where the rate of change does not follow the trigonometric sine function.
		The resulting pattern resembles the teeth of a saw blade.
		sinusoidal: A waveform in which the rate of change of a signal varies from zero to a maximum value in a smooth and regular manner that is described by the trigonometric sine function.
	www.ewh.ieee.org /soc/embs/comar/vdt.htm (5241 words)

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