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!

Benoit Descamps · Answer

Are 0 and 23 supposed to be the same?
If not then you should use $( sin(2ipi/24),cos(2ipi/24) )$ instead of $( sin(2ipi/23),cos(2ipi/23) )$ with $i in {0,...,23}$

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

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