Is there an identity for the cos( 1/3 x ) ?

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The discussion centers on the absence of a specific trigonometric identity for the cosine of a third-angle, specifically cos(1/3 x), in contrast to the established half-angle identities. Participants noted that while complex terms are involved in deriving such identities, the general form can accommodate any number, not just integers. The conversation highlights the challenges in solving cubic equations related to this topic.

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swampwiz
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It seems that this term comes up in solving the cubic equation. While there is the identity for the half-angle, there doesn't seem to be one for third-angle.
 
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Hi !

The identity involves complex terms :
 

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OK, I understand the general form. I didn't think to use an integer fraction in lieu of an integer. (Actually, it appears that *any* number could be used there.)
 

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