sine, cosine transformed cyclical features - am I losing information?

Question

If I use sine, cosine transformation for cyclical features (e.g. weekday or hour of the day), do I lose information if the first ordinal value was 0 respectively?

Assume hours of the day are encoded as follows: 0, 1, ..., 23

If I apply the sine, cosine transformation, I get 23 data points instead of 24 (cf. plot)

Am I losing information on the first ordinal value (0)?

Many thanks in advance!

Answer 1

Are 0 and 23 supposed to be the same?

If not then you should use $( \sin(2i\pi/24),\cos(2i\pi/24) )$ instead of $( \sin(2i\pi/23),\cos(2i\pi/23) )$ with $i \in \{0,...,23\}$