What is Sine: Definition and 521 Discussions

In mathematics, the sine is a trigonometric function of an angle. The sine of an acute angle is defined in the context of a right triangle: for the specified angle, it is the ratio of the length of the side that is opposite that angle, to the length of the longest side of the triangle (the hypotenuse). For an angle



x


{\displaystyle x}
, the sine function is denoted simply as



sin
⁡
x


{\displaystyle \sin x}
.More generally, the definition of sine (and other trigonometric functions) can be extended to any real value in terms of the length of a certain line segment in a unit circle. More modern definitions express the sine as an infinite series, or as the solution of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.
The sine function is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year.
The function sine can be traced to the jyā and koṭi-jyā functions used in Gupta period Indian astronomy (Aryabhatiya, Surya Siddhanta), via translation from Sanskrit to Arabic, and then from Arabic to Latin. The word "sine" (Latin "sinus") comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha.

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  1. R

    Easy yes or no answer sine law question.

    Homework Statement \ Is it ok to use sine law for this : A=sIN^-1(40SIN120/65.8) im not sure if this applies to the sin law angle restriction where the angle can't be over ??degrees?
  2. J

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  3. M

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  4. L

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  5. Ƒ

    Integral of sine to an even power

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  6. Z

    Image of upper half-plane under the inverse sine

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  7. M

    Sine Wave Addition: Standing Waves?

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  8. J

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  9. E

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  10. K

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  11. X

    Frequency Spectrum of a Real Sine Wave

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  12. morrobay

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  13. O

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  14. Phrak

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  15. H

    Calculating Forward and Backwards error of the sine function

    1. The sine function is given by the infinite series sin(x) = x - x3/3! + x5/5! + x7/7! + ... a) What are the forward and backward errors if we approximate the sine function by using only the first term in the series, for x = 0.1, 0.5, 1.0? b) Using the first two terms. Homework Equations...
  16. H

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  17. J

    Proof of additive property for sine

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  18. S

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  19. C

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  20. G

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  21. J

    RMS of square, sine and triangle waves

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  22. H

    What is the Fourier Sine Transform of 1?

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  23. K

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  24. A

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  25. N

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  26. K

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  27. K

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  28. R

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  29. A

    Trigonometric Identities for Sine and Cosine

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  30. P

    Why is Light in a Sine Wave Form?

    Why are light waves/X-rays/gamma rays/etc. in the form of sine waves, rather than, say, a zig zag wave, or even a straight line? I recently watched this youtube video explaining how to visualize ten dimensions: http://www.youtube.com/watch?v=JkxieS-6WuA&feature=related And wondered if photons...
  31. I

    Integration of 1/2 sin y dy from 0 to pi/2: Solution

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  32. B

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    Use the cosine and sine rules to determine the magnitude and direction of the resultant of a force of 11 kN acting at an angle of 50 degrees to the horizontal and a force of 6 kN acting at an angle of -30 degrees to the horizontal. helppp please
  33. I

    How to Prove the Sine Rule Using Cross Product?

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  34. S

    Sine of Uniformly Distributed Random Variable

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  35. L

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  36. H

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  37. N

    Propogation of error when taking sine inverse

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  38. D

    Quick question about the range of a sine function

    Homework Statement I am doing a proof about limits, and I need to know the range that sin(n^3-2n)/n is within for all n. Homework Equations The Attempt at a Solution I know that sin(n) is in between -1 and 1 for all n, so sin(n)/n would be in between -1/n and 1/n for all n...
  39. E

    Is the product of two sine functions always real-valued?

    Hi, I was playing around with Euler's Identity, and I found something (or at least I think I found something) interesting: It is a well known identity sin(z) = [exp(iz) - exp(-iz)]/(2*i), where z is any complex number, exp is the complex exponential function, and i is the imaginary...
  40. E

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  41. Y

    Expand the function f(x) = x^3 in a Fourier sine series

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  42. O

    Build In-Phase Sine Wave Generator 1KHz-12KHz Voltage Controlled

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  43. 0

    Signal that is a sine wave plus an offset

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  44. B

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  45. J

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  46. I

    Is a Sine Wave Always Transverse?

    hi all, pretty sure this is the wrong place to post this but it is a quick one so... is a sine wave always transverse? thanks
  47. G

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  48. D

    Newton's second law cosine and sine

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  49. P

    Power of a sine wave (electronics engineering)

    This is obviously an electronics question. In communication systems, to calculate the power of a sine wave, the formula below is used Power (Sine Wave) = 1/2 * (peak amplitude)^2 This formula is apparently a standard electronics formula. I'm trying to understand where it comes from. How...
  50. H

    Orthogonality of Sine and Cosine functions

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