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.

Let's free-hand Fourier transform! First, we sketch what we want on top of an actual sine function. Draw one period. We notice that in that period, the sine function is first too low, then too high, then too low, then too high again. That means that the difference between what we have and what we want has two tops and two bottoms, kindof like $\sin(2x)$. So we add that.
This time you have to plot the graph to see what happens. Let's try with $\sin(x) + 0.3\sin(2x)$. OK, we're getting the tilt we want, but on the way down the graph has this weird wavey thing. Back to the drawing board.
Now sketch the graph you had together with the graph you want. At least when I did this, the graphs crossed one another a number of times. $6$ to be exact, alternating which one is largest and which is smallest. Thus the difference has three maxes and three mins in this period, kindof like $\sin(3x)$. So we try to add that.
Now, with $\sin(x) + 0.3\sin(2x) + 0.65\sin(3x)$ it's starting to look good. You can probably tweak the coefficients here a bit to get something even better. Just keep going until you're happy. You can also add higher frequency terms if you want, which will give you more tilt. But it will get more difficult to gauge exactly how to compensate out the high frequency waving.
Alternatively, you could try to sketch the derivative you want, and do the same with that, only with cosines. Higher frequency waves will be more prominent then, and hopefully easier to correct for.
