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.. _fouc_s:
********************************************************************************
Foucaut Sinusoidal
********************************************************************************
.. image:: ./images/fouc_s.png
:scale: 50%
:alt: Foucaut Sinusoidal
The `y`-axis is based upon a weighted mean of the cylindrical equal-area and
the sinusoidal projections. Parameter :math:`n=n` is the weighting factor where
:math:`0 <= n <= 1`.
.. math::
\begin{array}
x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi)
y &= n \phi + (1 - n) \sin \phi
\end {array}
For the inverse, the Newton-Raphson method can be used to determine
:math:`\phi` from the equation for :math:`y` above. As :math:`n \rightarrow 0` and
:math:`\phi \rightarrow \pi/2`, convergence is slow but for :math:`n = 0`, :math:`\phi =
\sin^1y`
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