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- begin{subequations}
- begin{align}
- alpha_1 &=frac{1}{4}left[(L-1)^2 + tan ^2left(frac{2pi}{M}right)(L+1)^2right]\
- alpha_2 &= 1 \
- alpha_3 &=alpha_1\
- alpha_4 &=alpha_1
- end{align}
- end{subequations}
- The angle $theta$ values are
- begin{subequations}
- begin{align}
- theta_1 &= tan^{-1} left[frac{L+1}{L-1}tanleft(frac{2pi}{M}right)right]\
- theta_2 &= pi - theta_1\
- theta_3 &=theta_1\
- theta_4 &=frac{(M-2)pi}{M} - theta_1\[5pt]
- end{align}
- end{subequations}
- and
- begin{subequations}
- begin{align}
- phi_1 &= frac{pi}{2} - theta_1\
- phi_2 &= frac{2pi}{M}\
- phi_3 &= phi_1\
- phi_4 &= frac{2pi}{M} + theta_1
- end{align}
- end{subequations}
- documentclass[]{IEEEtran}
- usepackage{amsmath}
- usepackage{amssymb, amsfonts}
- usepackage{changepage}
- begin{document}
- begin{subequations}
- begin{align}
- alpha_1 &=frac{1}{4}left[(L-1)^2 + tan ^2left(frac{2pi}{M}right)(L+1)^2right]\
- alpha_2 &= 1 \
- alpha_3 &=alpha_1\
- alpha_4 &=alpha_1
- end{align}
- end{subequations}
- The angle $theta$ values are
- begin{adjustwidth}{-15.2mm}{0mm}
- begin{subequations}
- begin{align}
- theta_1 &= tan^{-1} left[frac{L+1}{L-1}tanleft(frac{2pi}{M}right)right]\
- theta_2 &= pi - theta_1\
- theta_3 &=theta_1\
- theta_4 &=frac{(M-2)pi}{M} - theta_1\[5pt]
- end{align}
- end{subequations}
- end{adjustwidth}
- and
- begin{adjustwidth}{-42mm}{0mm}
- begin{subequations}
- begin{align}
- phi_1 &= frac{pi}{2} - theta_1\
- phi_2 &= frac{2pi}{M}\
- phi_3 &= phi_1\
- phi_4 &= frac{2pi}{M} + theta_1
- end{align}
- end{subequations}
- end{adjustwidth}
- end{document}
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