# Cosine of Half Angle for Spherical Triangles/Mistake

Jump to navigation
Jump to search

## Contents

## 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: $5.99$