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# Topic: Trigonometric function

###### In the News (Tue 18 Jun 19)

 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   (809 words)

 Trigonometric function - Wikinfo In mathematics, the trigonometric functions are functions of an angle important when studying triangles and modeling periodic phenomena. 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 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   (5797 words)

 Graphs of Basic Trigonometric Functions The graphs and properties such as domain, range, vertical asymptotes of the 6 basic trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and csc (x) are explored using an applet. Once you finish the present tutorial, you may want to go through a self test on trigonometric graphs. More references and links related to trigonometric functions and their properties. www.analyzemath.com /GraphBasicTrigonometricFunctions/GraphBasicTrigonoFunction.html   (433 words)

 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   (0 words)

 Trigonometric function Encyclopedia Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. The sine and the cosine functions are used to describe the simple harmonic motion, that is used to model diverse natural phenomena, like for example, the mass in a string movement and, for small angles, the mass on a pendulum movement. Trigonometric functions also prove to be useful in the study of general periodic functions. www.hallencyclopedia.com /topic/Trigonometric_function.html   (4471 words)

 math lessons - Trigonometric function In mathematics, the trigonometric functions are functions of an angle, important when studying triangles 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.mathdaily.com /lessons/Trigonometric_function   (2881 words)

 Math.com Trig Overview   (Site not responding. Last check: ) Under its simplest definition, a trigonometric (literally, a "triangle-measuring") function, is one of the many functions that relate one non-right angle of a right triangle to the ratio of the lengths of any two sides of the triangle (or vice versa). Furthermore, the functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). Therefore, the tangent function is the same as the quotient of the sine and cosine functions (the tangent function is still fairly handy). www.math.com /tables/algebra/functions/trig/overview.htm   (886 words)

 Trigonometric function In mathematics, the trigonometric functions are functions of an angle important when studying triangles and modeling periodic phenomena. 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 trigonometric functions are also important outside of the study of triangles. www.black-science.org /wikipedia/t/tr/trigonometric_function.html   (1243 words)

 Trigonometric rational function - Wikipedia, the free encyclopedia In mathematics, a trigonometric rational function is a rational function in the functions sin θ and cos θ. Equivalently, it is a ratio of trigonometric polynomials. Stating this more accurately, in a case of a non-trivial limit (indeterminate form) of such a rational function and a simple (not repeated) zero of the denominator, it is permissible to replace sin nθ by n, and cos nθ directly by its value 1. en.wikipedia.org /wiki/Trigonometric_rational_function   (635 words)

 [No title]   (Site not responding. Last check: ) In mathematics, the trigonometric functions are functions of an angle important when studying triangles and modeling periodic phenomena. The six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin. The trigonometric functions are also important outside of the study of triangles. www.wikiwhat.com /encyclopedia/t/tr/trigonometric_function.html   (1317 words)

 Trigonometric function - Wikipedia, the free encyclopedia 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. 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   (3865 words)

 PlanetMath: determining signs of trigonometric functions There are at least two mnemonic devices for determining the sign of a trigonometric function at a given angle. If the sign of the trigonometric function is different in the two boundary quadrants, then the value of the trigonometric function applied to the angle is either 0 or undefined. This is version 3 of determining signs of trigonometric functions, born on 2006-07-22, modified 2006-07-22. planetmath.org /encyclopedia/DeterminingSignsOfTrigonometricFunctions.html   (442 words)

 Vector Addition   (Site not responding. Last check: ) The sine function relates the sine of an angle to the ratio of the length of the side opposite the angle to the length of the hypotenuse. The cosine function relates the cosine of an angle to the ratio of the length of the side adjacent the angle to the length of the hypotenuse. The tangent function relates the tangent of an angle to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. www.glenbrook.k12.il.us /gbssci/phys/Class/vectors/u3l1b.html   (1638 words)

 The Trig Functions - Overview "triangle-measuring") function, is one of the many functions that relate one non-right angle of a right triangle to the ratio of the lengths of any two sides of the triangle (or vice versa). Furthermore, the functions are usually abbreviated: sine (sin), cosine (cos), tangent (tan) cosecant (csc), secant (sec), and cotangent (cot). Therefore, the tangent function is the same as the quotient of the sine and cosine functions (the tangent function is still fairly handy). www.math2.org /math/algebra/functions/trig/overview.htm   (878 words)

 Trigonometric function Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. The sine and the cosine functions, for example, are used to describe the simple harmonic motion, which models many natural phenomena, such as the movement of a mass attached to a spring and, for small angles, the pendular motion of a mass hanging by a string. Trigonometric functions also prove to be useful in the study of general periodic functions. libraryoflibrary.com /E_n_c_p_d_Sine.html   (7792 words)

 Hyperbolic function Summary   (Site not responding. Last check: ) The exponential function, on which the hyperbolic functions are based, is a singly periodic elliptic function that means the modulus of periodicity is 2. The inverse hyperbolic functions are denoted as sinh In mathematics, the hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. www.bookrags.com /Hyperbolic_function   (1457 words)

 Signs of Trigometric Function The cosine function, abbreviated cos, is the ratio of the adjacent to the hypotenuse sides. The cosecant function, abbreviated csc, is the inverse function to the sin function. The secant function, abbreviated sec, is the inverse function to the cos function. www.cgtcollege.org /mat193/signs.htm   (2569 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)

 Trigonometric function: Definition and Links by Encyclopedian.com ...are holomorphic on C,and so are the trigonometric functions and the exponential function.(The trigonometric...0}.The inverse trigonometric functions likewise have seams and are holomorphic everywhere... ...can be seen as analogs of the trigonometric functions (which have a single period only). Formally, an...a meromorphic function f defined on C for which there exist two non-zero complex numbers a and b... www.encyclopedian.com /si/Sine.html   (1586 words)

 Online Math Calculators and Solvers Calculate the inverse trigonometric function arcsin(x) in radians and degrees. Calculate inverse trigonometric function arccos(x) in radians and degrees. Calculate inverse trigonometric function arctan(x) in radians and degrees. www.analyzemath.com /Calculators.html   (989 words)

 Trigonometric Function (Using Simulink) The Trigonometric Function block performs numerous common trigonometric functions. The block output is the result of the function operating on the input or inputs. Use the Trigonometric Function block instead of the Fcn block when you want dimensionalized output because the Fcn block can produce only scalar output. www.phys.ufl.edu /docs/matlab/toolbox/simulink/ug/trigonometricfunction.html   (119 words)

 Trigonometric and Inverse Trigonometric Function Gallery The following is a gallery of demos illustrating selected families of trigonometric functions These animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. A demo that provides a visual development of the sine and cosine functions and their graphs by 'wrapping' around a circle is available at mathdemos.gcsu.edu. At http://www.univie.ac.at/future.media/moe/galerie/wfun/wfun.html under the heading Function 2 are applets and recognition puzzles for graphs of sine and cosine. mathdemos.gcsu.edu /mathdemos/family_of_functions/trig_gallery.html   (495 words)

 Sine Function To deeply understand the effects of each parameter on the graph of the function, we change one parameter at the time at the start. Once you finish the present tutorial, you may want to work through a self test on trigonometric graphs. 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)

 12.5.2. Trigonometric and Related Functions The way in which they are extended to operate on complex numbers makes the trigonometric connection clear. is a rational function, but it may be irrational for complex arguments. These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument z as follows: cltl2.lisp.se /cltl/clm/node128.html   (0 words)

 Mathematics Tutorials and Problems (with applets) The site includes several java applets to investigate Graphs of Functions, Equations, and Algebra. Calculus Tutorials and Problems and Questions with answers on topics such as limits, derivatives, integrals, natural logarithm, runge kutta method in differential equations, the mean value theorem and the use of differentiation and integration rules are also included. Trigonometry Tutorials and Problems for Self Tests on sine, cosine, tangent, secant functions, trigonometric identities and formulas are also included. www.analyzemath.com   (460 words)

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