Equation of a “tilted” sine

I would like to know what’s the equation of a “tilted” sine, that looks like this (no idea how to show it better).

enter image description here

I remember first seeing this waveform in some kind of sound synthesizer, where one of the knobs for controlling shape of the sine was doing just what im looking for – gradually turning sine to sawtooth and vice versa.

I tried using fourier series on a sawtooth wave, and getting a couple of first sines together, but the result doesn’t have that smoothness.

Answer

You can try this :

y=sin(x+yn)

Here nR{0}. Positive n will “tilt” the graph left side, while negative n, right side.

For example,

When n=1, y=sin(x+y)

enter image description here

When n=2, y=sin(x+y2)

enter image description here

When n=10, y=sin(x+y10)

enter image description here

As n, y=sin(x)

enter image description here

Attribution
Source : Link , Question Author : Lugi , Answer Author : Jaideep Khare

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