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A Functional Equation Characterising the Sine

Published online by Cambridge University Press:  03 November 2016

R. A. Rosenbaum  and
S. L. Segal
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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

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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