# What is Sine: Definition and 520 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. ### B Sine rule for Resultant Vectors

Hello , please can anyone explain to me the difference and use between these two sine rules: a/sinA = n/sinB= c/sinC and sinA/a = sinB/c= sinC/c. Thanks and God bless you.
2. ### Why are the paths of our cosmic explorations, pretty?

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3. ### Derivation or proof of derivative sin (x)

How do I do this from here without using the derivatives of sin or cos ?
4. ### Can a Square Wave Tachometer Drive be Powered by a Sine Waveform?

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5. ### Is it possible to solve relative velocity problems without sine law?

I was able to solve this question successfully by utilizing the sine and cosine law however my instructor said I was only allowed to utilize the vector component method, I am unsure how to complete this question using the vector component method as we have two unknowns(those being the angle of...
6. ### Fourier sine and cosine transforms of Heaviside function

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10. ### B Happy Christmas: Is it Really True?

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11. ### I Equation to graph a sine wave that acts like a point on a unit circle

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12. ### I Phase Shift of a Sine Wave

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13. ### A Fourier Transform of an exponential function with sine modulation

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14. ### MHB Definite integral involving sine and hyperbolic sine

Calculate $\displaystyle \int_0^{\infty} \frac{\sin x}{\cos x + \cosh x}\, \mathrm dx.$
15. ### B RC Low Pass Circuit Sine Wave Response

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16. ### MHB Linear combination of sine and cosine function

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17. ### MHB Trigonometric of tangent and sine functions

Simplify $\left(\tan \dfrac{2\pi}{7}-4\sin \dfrac{\pi}{7}\right)\left(\tan \dfrac{3\pi}{7}-4\sin \dfrac{2\pi}{7}\right)\left(\tan \dfrac{6\pi}{7}-4\sin \dfrac{3\pi}{7}\right)$.
18. ### Odd and even extension of sine function

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20. ### MHB Can You Meet the Sine Function Challenge?

Let $a,\,b$ and $c$ be real numbers such that $\sin a+\sin b+\sin c\ge \dfrac{3}{2}$. Prove that $\sin \left(a-\dfrac{\pi}{6}\right)+\sin \left(b-\dfrac{\pi}{6}\right)+\sin \left(c-\dfrac{\pi}{6}\right)\ge 0$.
21. ### MHB Computing the value of sine function accurately

Hi all Simple question: How I can compute the value of $$a = \sin \left( 2017 \sqrt[5]{2} \right)$$ under following assumptions: No use of advanced numerical libraries is allowed. Only accepted operations are: comparisons, absolute value, addition, subtraction, multiplication and division...
22. ### I Exact Expression for Sine of 1 Degree

For example, $$Sin(15)= \frac {(\sqrt 6 - \sqrt 2)} 4$$ and $$Sin(3)=\frac {(\sqrt 6 (\sqrt 5 -1)(3+\sqrt 3)} {48} -\frac {\sqrt 3 (3-\sqrt 3 )\sqrt{ 5+\sqrt 5 }} {24}$$ What about ##Sin(1)##?
23. ### A Sine Dipole formation using two hydrophones

Hi all. I am trying to do MATLAB simulations for generation of SINE Dipole using two hydrophones spaced distance 'd' apart for signal coming from direction 'DOA'. The MATLAB code is given below. The confusion is that there is constant phase difference of 90 degree b/w SINE Dipole generated using...
24. ### I Determining the Equation of a Sine and Cosine Graph that speeds up

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25. ### B What is the speed of a photon traveling along the sine function?

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49. ### What is the mistake in calculating the integral of the absolute sine function?

Homework Statement \int_0^{2018 \pi} \lvert \sin(2018x) \lvert \mbox{d}x Homework EquationsThe Attempt at a Solution So the period is: \frac{2 \pi}{ 2018} Each "hump" of the sine has an area of 2 so if I count the number of humps I am done. In one period of an absolute sine function the...
50. ### Photoelectric effect , Superposition of sine waves

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