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-\sin_zx &=& +\sin_{z^{-1}}x &=& +\exp_5^{(1)}x-\exp_4^{(4)}x-\phi'\exp_4^{(3)}x+\phi'\exp_4^{(2)}x &\leftarrow[~~0~~,-1~,-\phi',+\phi',+1~]\\
&& -\cos_{z^{-1}}x &=& +\exp_5^{(2)}x-\exp_4^{(5)}x-\phi'\exp_4^{(4)}x+\phi'\exp_4^{(3)}x &\leftarrow[-1~,-\phi',+\phi',+1~,~~0~~]\\
&=& (+\sin_{z^{-1}}x)'' &=& +\exp_5^{(3)}x-\exp_4^{(0)}x-\phi'\exp_4^{(5)}x+\phi'\exp_4^{(4)}x &\leftarrow[-\phi',+\phi',+1~,~~0~~,-1~]\\ &=& (-\cos_{z^{-1}}x)'' &=& +\exp_5^{(4)}x-\exp_4^{(1)}x-\phi'\exp_4^{(0)}x+\phi'\exp_4^{(5)}x &\leftarrow[+\phi',+1~,~~0~~,-1~,-\phi']\\
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-\cos_zx && &=& -\exp_5^{(0)}x+\exp_4^{(3)}x+\phi'\exp_4^{(2)}x-\phi'\exp_4^{(1)}x &\leftarrow[-1~,~~0~~,+1~,+\phi',-\phi']\\
