Hostname: page-component-77c89778f8-swr86 Total loading time: 0 Render date: 2024-07-22T00:27:25.368Z Has data issue: false hasContentIssue false
  • English
  • Français

A Functional Equation Characterising the Sine

Published online by Cambridge University Press:  03 November 2016

R. A. Rosenbaum  and
S. L. Segal
Get access Rights & Permissions [Opens in a new window]

Extract

Recent articles on equations characterising the trigonometric functions ([1], [2]) prompt a consideration of still another equation, which might be classified under the heading of “Students’ Mathematical Mythology” In [3], Mr. Heafford multiplies the “obvious” sin (x + y) = sin x + sin y by the equally “clear” sin (x − y) = sin x − sin y to obtain the (correct!) result, sin (x+y) sin(x − y) = sin2x − sin2y.

Type
Research Article
Information
The Mathematical Gazette , Volume 44 , Issue 348 , May 1960 , pp. 97 - 105
Copyright
Copyright © Mathematical Association 1960

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Parameswaran, S., “Trigonometry Retold”, Mathematical Gazette, Vol. XLII (1958) pp. 81–3.CrossRefGoogle Scholar
2. Vaughan, H. E., “Characterization of the sine and cosine”, The American Mathematical Monthly, Vol. 62 (1955), pp. 707–13.CrossRefGoogle Scholar
3. Heafford, Phillip, Mathematics for Fun (Hutchinson), p. 49.Google Scholar