Thanks for your reply.
In practice I found the following:

The train error would be significantly higher when I use the additional sine and cosine as inputs, in comparison to just using the 1d signal.
I hypothesized that the above could be due to the fact that my 1d input signal is actually on a scale of 0-3000 or so, whereas the sine and the cosine representing the hour of the day are only on a scale of 0 to 1.
To address #2, I normalized the 1d signals to a range of 0 to 1. However, now, I observe that my predictions during the training phase have a lot of negative values. This is odd since my actual 1d input signal and the output are both non-negative in nature.