Cosine of Half Angle for Spherical Triangles/Mistake
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Source Work
1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables
- Chapter $5$: Trigonometrical Functions:
- Relationships between Sides and Angles of a Spherical Triangle
This mistake can be seen in the edition as published by Schaum: ISBN 0-07-060224-7 (unknown printing).
Mistake
Let $\triangle ABC$ be a spherical triangle on the surface of a sphere whose center is $O$.
Let the sides $a, b, c$ of $\triangle ABC$ be measured by the angles subtended at $O$, where $a, b, c$ are opposite $A, B, C$ respectively.
Then:
- $\cos \dfrac A 2 = \sqrt {\dfrac {\sin s \, \map \sin {s - c} } {\sin b \sin c} }$
where $s = \dfrac {a + b + c} 2$.
Correction
The correct formula is:
- $\cos \dfrac A 2 = \sqrt {\dfrac {\sin s \, \map \sin {s - a} } {\sin b \sin c} }$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: $5.99$