Editing Transverse Mercator projection (section)

===The relation between the graticules===
The angles of the two graticules are related by using [[spherical trigonometry]] on the spherical triangle NM′P defined by the true meridian through the origin, OM′N, the true meridian through an arbitrary point, MPN, and the great circle WM′PE. The results are:<ref name=merc/>
:<math>
\begin{align}
\sin\varphi'&=\sin\lambda\cos\varphi,\\
\tan\lambda'&=\sec\lambda\tan\varphi.
\end{align}
</math>