Functions Definition and 1000 Threads

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others. They are among the simplest periodic functions, and as such are also widely used for studying periodic phenomena through Fourier analysis.
The trigonometric functions most widely used in modern mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. Each of these six trigonometric functions has a corresponding inverse function (called inverse trigonometric function), and an equivalent in the hyperbolic functions as well.The oldest definitions of trigonometric functions, related to right-angle triangles, define them only for acute angles. To extend these definitions to functions whose domain is the whole projectively extended real line, geometrical definitions using the standard unit circle (i.e., a circle with radius 1 unit) are often used. Modern definitions express trigonometric functions as infinite series or as solutions of differential equations. This allows extending the domain of sine and cosine functions to the whole complex plane, and the domain of the other trigonometric functions to the complex plane from which some isolated points are removed.

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  1. M

    Help with Trig Function: Sec(2x)csc(x)sin(2x) and C=cosx

    Homework Statement Let C=cosx. Write sec(2x)csc(x)sin(2x) as a function of C. The Attempt at a Solution Am I on the right track 1/cos(2x) * 1/sin(x) * 2sin(x)cos(x) 1/(cos^2(x)-sin^2(x)) * `1/(sqrt(1-cos^2(x)) * 2(sqrt(1-cos^2(x))cos(x) What would i do from here?
  2. Evangeline101

    Sinusoidal Functions: Niagara Falls Skywheel....

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  3. dreens

    I Orthogonal 3D Basis Functions in Spherical Coordinates

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  4. M

    Find the Domain and Range of Functions with Given Domain and Range Values

    Homework Statement Suppose f is a function with domain [-2,10] and range [5,10]. Find the domain and range of the following functions. (a) f(2x+4) (b) 2f(x)+4 The Attempt at a Solution [/B] Would I just substitute the in the domain and range values to find the answer?
  5. M

    I Relations & Functions: Types, Examples, Homomorphism

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  6. A

    Use of floor and ceiling functions in physics problems

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  7. K

    Properties of Wave Functions and their Derivatives

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  8. orion

    I Understanding the Transition Functions for S^1 Using Atlas Charts

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  9. orion

    I Boundedness and continuous functions

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  10. Rectifier

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  11. E

    Units of constants in transfer functions?

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  12. J

    I Procedurally generated polynomial functions

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  13. awholenumber

    I Question ,trigonometric identities equation and functions ?

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  14. Evangeline101

    Number of hours of daylight - Periodic functions.

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  15. P

    B Sets and functions that gain more structure with context

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  16. I

    MATLAB Transforming part of matlab code to Fortran90

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  17. MrDickinson

    I Can someone me simplify this expression....

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  18. T

    I Smoothness of Discrete Functions

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  19. F

    MHB Finding Functions: Amplitude, Period, Frequency, Phase Angle

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  20. J

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  21. anemone

    MHB Evaluate a floor function involving trigonometric functions

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  22. V

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  23. H

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  24. KF33

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  25. KF33

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  26. KF33

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  27. R

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  28. sunrah

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  29. S

    MHB What Are Singly and Doubly Indexed Functions in Philosophy?

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  30. P

    I Analytic functions of analytic functions

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  31. H

    I Graphs of inverse trigonometric vs inverse hyperbolic functions

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  32. Muthumanimaran

    Are Products of Dirac Delta Functions Well-Defined?

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  33. Muthumanimaran

    What is the product of two Dirac delta functions

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  34. D

    Solving functions for S in a q-q* Hamilton-Jacobi diffeq

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  35. C

    No of ordered pairs satisfying this equation

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  36. ChrisVer

    A Trying several fits with only 2 functions?

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  37. B

    Show these functions are 2 pi periodic

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  38. alexandria

    Periodic Functions Homework: Daylight Hours

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  39. Evangeline101

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  40. Evangeline101

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  41. G

    MHB Question related to inverse sine functions

    Please guide why answers are different in following two cases and which one is correct? Case 1. sin-1 ( – 1/2 ) – sin-1 (– 1) = 7π/6 – 3π/2 = – π/3 Case 2. sin-1 ( – 1/2 ) – sin-1 (– 1) = – sin-1 ( 1/2 ) + sin-1 (1)...
  42. Danielm

    Proving the Bijectivity of a Function: σ : Z_11 → Z_11 | Homework Solution

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  43. D

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  44. D

    I Are f(x) = xcos(x) and g(x) = cos(x) Linearly Independent?

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  45. U

    Periodic Functions: Find Fundamental Period & Graph Solution

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  46. Drakkith

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  47. L

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  48. Y

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  49. E

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  50. W

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