Editing Spherical trigonometry (section)

===Napier's rules for quadrantal triangles===
[[File:Spherical trigonometry Napier quadrantal 01.svg|center|thumb|300px|A quadrantal spherical triangle together with Napier's circle for use in his mnemonics]]

A quadrantal spherical triangle is defined  to be a spherical triangle in which one of the sides subtends an angle of {{pi}}/2 radians at the centre of the sphere: on the unit sphere the side has length {{pi}}/2. In the case that the side  {{mvar|c}} has length {{pi}}/2 on the unit sphere the equations governing the remaining sides and angles may be obtained by applying the rules for the right spherical triangle of the previous section to the polar triangle {{math|△''A'B'C' ''}} with sides {{mvar|a', b', c'}} such that {{math|1=''A' ''= {{pi}} − ''a''}}, {{math|1=''a' ''= {{pi}} − ''A''}} etc. The results are:
<math display="block">\begin{alignat}{4}
  &\text{(Q1)}&\qquad  \cos C &= -\cos A\,\cos B,
&\qquad\qquad
  &\text{(Q6)}&\qquad \tan B &= -\cos a\,\tan C,\\
  &\text{(Q2)}& \sin A &= \sin a\,\sin C,
&&\text{(Q7)}& \tan A &= -\cos b\,\tan C,\\
  &\text{(Q3)}& \sin B &= \sin b\,\sin C,
&&\text{(Q8)}& \cos a &= \sin b\,\cos A,\\
  &\text{(Q4)}& \tan A &= \tan a\,\sin B,
&&\text{(Q9)}& \cos b &= \sin a\,\cos B,\\
  &\text{(Q5)}& \tan B &= \tan b\,\sin A,
&&\text{(Q10)}& \cos C &= -\cot a\,\cot b.
\end{alignat}</math>