# 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).

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.

You can try this :

Here $n \in \mathbb R -\{0\}$. Positive $n$ will “tilt” the graph left side, while negative $n$, right side.

For example,

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

When $n=2$, $y=\sin \left( x+\dfrac {y}{2} \right)$

When $n=10$, $y=\sin \left( x+\dfrac {y}{10} \right)$

As $n \to \infty$, $y=\sin(x)$