How can I generate a sinewave with Arduino Uno? I would like to generate a sine wave with my Arduino Uno. As far as I know, there is no library for Uno to generate such a signal (correct me if I'm wrong), so the only option available is to write a function to generate the signal from scratch.

As far as my understanding of digital electronics goes, I believe it is possible to generate a sine wave signal by using PWM and varying the duty cycle accordingly. However, this route seems to me quite long, what other options do I have?
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.