"Sum to Product" Trigonometric identity does not work


by CraigH
Tags: identity, sum to product, trigonometric
CraigH
CraigH is offline
#1
Apr27-13, 02:34 PM
P: 190
Hi,

The identity

[itex]sin(u) + sin(v) = 2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2})[/itex]
http://en.wikipedia.org/wiki/List_of...uct_identities

Does not always work. I put the equation :

[itex](sin(u) + sin(v)) - (2 * sin (\frac{u+v}{2}) * cos(\frac{u-v}{2}))[/itex]

With u equal to -4.1 and v equal to 99 into wolfram alpha and it gave me the answer -1.11022x10^-16
http://www.wolframalpha.com/input/?i...9%2F2%29%29%29

If the identity is true, shouldn't the answer always be 0?

What's going on here?

Thanks
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HS-Scientist
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#2
Apr27-13, 02:44 PM
P: 181
It seems like a rounding error to me. You can verify that the identity is in fact always true by using the half angle and angle addition formulae.
micromass
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#3
Apr27-13, 02:49 PM
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The problem is not that the formula doesn't work, but with the fact that your calculator is incapable of precisely calculating the sine or cosine of an angle.

CraigH
CraigH is offline
#4
Apr27-13, 02:56 PM
P: 190

"Sum to Product" Trigonometric identity does not work


Ah okay, thank you for answering.
One thing though... If wolfram alpha knows that it can only calculate the sine or cosine of an angle to a certain precision, shouldn't it give the final answer to that precision, or less, so that it avoids giving misleading answers like the one it gave me.
micromass
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#5
Apr27-13, 02:58 PM
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Quote Quote by CraigH View Post
Ah okay, thank you for answering.
One thing though... If wolfram alpha knows that it can only calculate the sine or cosine of an angle to a certain precision, shouldn't it give the final answer to that precision, or less, so that it avoids giving misleading answers like the one it gave me.
It would be better if they did that. But I've never seen a calculator doing it. They rather count on the users to know about the fallibility of the program.


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