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en.wikipedia.org/wiki/Sine_wave

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing and many other fields.

jwilson.coe.uga.edu/EMAT6680/Dunbar/Assignment1/sine_curves_KD.html

Assignment 1: Exploring Sine Curves. by Kristina Dunbar, UGA In this assignment, we will be investigating the graph of the equation y = a sin (bx + c) using different values for a, b, and c. In the above equation, a is the amplitude of the sine curve; b is the period of the sine curve; c is the phase shift of the sine curve .

www.brightstorm.com/.../find-an-equation-for-the-sine-or-cosine-wave

When you're finding the equation for the graph of a sine or cosine curve, you have to first try recognize whether it's a sine or cosine curve. A sine curve would start at the origin like this. It starts on an intercept whereas a cosine curve starts at its max or its mean if it's reflected.

www.thefreedictionary.com/sine+curve

Define sine curve. sine curve synonyms, sine curve pronunciation, sine curve translation, English dictionary definition of sine curve. sine curve The equation for this sine curve is y = sin x. n. The graph of the equation y = a sin bx, where a and b are constants.

en.wikipedia.org/wiki/Sine

The arc length of the sine curve from 0 to x is the above number divided by times x, plus a correction that varies periodically in x with period . The Fourier series for this correction can be written in closed form using special functions, but it is perhaps more instructive to write the decimal approximations of the Fourier coefficients.

www.onemathematicalcat.org/Math/Precalculus_obj/givenAmpPerPSWriteEq.htm

In the prior section, you learned how to find the amplitude, period, and phase shift of a given (generalized) sine or cosine curve. In this section, you will write an equation of a curve with a specified amplitude, period, and phase shift. Sample question: Write an equation of a sine curve with amplitude $\,5\,$, period $\,3\,$, and phase shift $\,2\,$.

www.purplemath.com/modules/grphtrig.htm

The amplitude has changed from 1 in the first graph to 3 in the second, just as the multiplier in front of the sine changed from 1 to 3. This relationship is always true: Whatever number A is multiplied on the trig function gives you the amplitude (that is, the "tallness" or "shortness" of the graph); in this case, that amplitude number was 3 .

www.mathguide.com/lessons2/GraphingTrig.html

So, the curve has a y-intercept of zero (because it is a sine curve it passes through the origin) and it completes one cycle in 120 degrees. This is the graph of the sine curve. This particular interval of the curve is obtained by looking at the starting point (0,0) and the end point (120,0).

jwilson.coe.uga.edu/emt668/EMT668.Folders.F97/Feller/sine/assmt1.html

The last variation in this equation will be c. In the first equation, y = sin x, c is equal to zero. Look at the graph on the left to see that curve as well as the curve of the equation y = sin (x + 2). Notice that the new curve is shifted two units to the left of the original one.

community.ptc.com/t5/Part-Modeling/Equations-for-Curves-and-more/td-p/446997

After the Equations section see the section title Links to find PlanetPTC discussions and videos that have demonstrated and, in some cases, explained the curve from equation command in more detail with ways to incorporate relations and parameters.