How can the sum of three cosines equal 1?

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SUMMARY

The discussion focuses on proving the relationship where the sum of three cosines equals 1, as outlined in the document from UCSB. The key approach involves using the coordinates of point P, defined as (cos α1, cos α2, cos α3)d, and applying the Pythagorean theorem to derive the desired relation. This method effectively demonstrates the geometric interpretation of the cosine functions in relation to their sum.

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  • Understanding of trigonometric functions, specifically cosine.
  • Familiarity with the Pythagorean theorem.
  • Basic knowledge of geometric coordinates.
  • Ability to interpret mathematical proofs and relations.
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Mathematics students, educators, and anyone interested in trigonometric identities and their geometric interpretations will benefit from this discussion.

Gunthi
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If OP=d, the coordinates of P are (cos α1,cos α2,cos α3)d. Now, express the length of OP using Pythagoras and you get the desired relation.
 
Norwegian said:
If OP=d, the coordinates of P are (cos α1,cos α2,cos α3)d. Now, express the length of OP using Pythagoras and you get the desired relation.

Got it! Thanks!
 

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