How can I generate a sinewave with Arduino Uno?
As far as I know, there is no library for Uno to generate such a
  signal (correct me if I'm wrong)


You are wrong, there is Mozzi, the sound synthesis library for
Arduino. It works essentially along the lines sketched by uint128_t.
Take a look at the Sinewave.ino for an example on how to make a
(lookup table-based) sine wave. It can also do much more.

In its default mode, Mozzi works with a 16,384&nbsp;Hz sample rate and a
32,768&nbsp;Hz (not audible) PWM frequency.