Who Discovered the Trig Sum Formulas?

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The discussion centers on the derivation of the trigonometric sum formulas, specifically sin(a + b), sin(a - b), cos(a + b), and cos(a - b). A humorous claim is made that Julia Ward Howe derived these formulas in 1861, linking them to the Battle Hymn of the Republic. Participants express confusion over the joke, with some requesting more serious commentary on the topic. The conversation highlights the historical context of the formulas but lacks substantial information on their actual mathematical origins. Overall, the thread mixes humor with a desire for serious discussion about trigonometric history.
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sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

Who first derived them? When, and how?

Thanks
 
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ImAnEngineer said:
Who first derived them? When, and how?

Not how, but Howe … Julia Ward Howe, in 1861, derived them, and they became a Civil War marching song, to the tune now known as the Battle Hymn of the Republic. :wink:
 
tiny-tim said:
Not how, but Howe … Julia Ward Howe, in 1861, derived them, and they became a Civil War marching song, to the tune now known as the Battle Hymn of the Republic. :wink:
If it's a joke... sorry but I don't get it.
 
ImAnEngineer said:
If it's a joke... sorry but I don't get it.

:rolleyes:

try singing it! :smile:
 
tiny-tim said:
:rolleyes:

try singing it! :smile:

Struggling to get a nice melody... :P

Any serious comments?
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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