Combining Cos Functions

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Cos (A) + Cos (A + 2pi/3) + Cos (A + 4pi/3)

Im just not sure how your meant to combine all three, it generally confuses me. Your supposed to expand and simplify but i dont get it.

Any help would be appreciated...
Thanks

Edit: I thought about it a bit more and after i expanded it out and canceled a few terms i got:

Cos (A) - 0.5 Cos(A) - 0.5Cos(A)

Now my question is does this cancel down to zero?

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Yep.

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Re: Combining Cos Functions

guy101 wrote:

Cos (A) + Cos (A + 2pi/3) + Cos (A + 4pi/3)

Im just not sure how your meant to combine all three, it generally confuses me....

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

The 2nd term:
Cos(A + 2pi/3) = Cos(A)Cos(2pi/3) - sin(2pi/3)sin(A)
= Cos(A)(-.5) - (.866)sin(a)

The 3rd term:
Cos(A + 4pi/3) = Cos(A)Cos(4pi/3) - sin(4pi/3)sin(A)
= Cos(A)(-.5) - (-.866)sin(a)

These add to - Cos(A), which, together with the first term sums to zero.

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Thanks for the confirmation, helps me sleep at night.

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Combining Cos Functions

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