Can addition formula be applied to more than 2 sums?

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Homework Help Overview

The discussion revolves around the application of the cosine addition formula, specifically whether it can be extended to sums involving more than two angles, such as cos(A+B+C). Participants are exploring the logic behind the formula and its potential for multiple angles.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants are questioning the validity of applying the cosine addition formula to three angles and discussing the steps involved in expanding the expression. There is an exploration of how to handle the addition of angles beyond two.

Discussion Status

Some guidance has been offered regarding the expansion of cos(A+B+C) by suggesting to first expand cos((A+B) + C). Participants are actively engaging with the concept, and there is a recognition of the need to apply the addition formula iteratively.

Contextual Notes

There is a mention of uncertainty regarding the application of the formula to multiple angles, and participants are considering the logic behind the formula rather than seeking a definitive solution.

lax1113
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Homework Statement



Not an actual problem, but to help solve my homework, would cos(A+B+C)=
CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny)

I was unsure if this can be applied to multiple digits or only 2.



I know I could plug in numbers to test, but I was wondering about the logic behind this.
 
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lax1113 said:

Homework Statement



Not an actual problem, but to help solve my homework, would cos(A+B+C)=
CosACosBCosC-SinASinBSinC (Cos(x+y)=cosxcoxy-sinxsiny)

I was unsure if this can be applied to multiple digits or only 2.



I know I could plug in numbers to test, but I was wondering about the logic behind this.
No, that's not it.

Expand cos((A+B) + C) first, and then expand the factors with cos(A+B) and sin(A+B).
 
I see.

So Cos(A+B+C) =

cos((CosAcosB-sinAsinB)+C)

then use the value from the first portion in another addition formula with C?
 

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