Cosine addition trouble

[MarcaNL]

Hello, does anyone know how to rewrite equation (1) according to the format shown in equation (2)?

-A cos(x+b)+ C cos(x+d) (1)

R cos(x+e) (2)

If so, how do you calculate R?

 

[blamocur]

Have you tried using identity [imath]\cos \alpha = e^{i\alpha}[/imath] ?

 

[Deleted member 4993]

Hello, does anyone know how to rewrite equation (1) according to the format shown in equation (2)?

-A cos(x+b)+ C cos(x+d) (1)

R cos(x+e) (2)

If so, how do you calculate R?

Please review your question - carefully - for typos. Then repost - if there is a typo.

Let us know if there are NO TYPOs.

 

[blamocur]

Have you tried using identity [imath]\cos \alpha = e^{i\alpha}[/imath] ?

Ooops -- I meant [imath]\cos\alpha = \Re e^{i\alpha}[/imath], where [imath]\Re[/imath] stands for the real part of a complex number.

 

[Dr.Peterson]

Hello, does anyone know how to rewrite equation (1) according to the format shown in equation (2)?

-A cos(x+b)+ C cos(x+d) (1)

R cos(x+e) (2)

If so, how do you calculate R?

My first thought was to use the angle-sum identities to expand (1) into a sum of multiples of sin(x) and cos(x), then use whatever method you are familiar with (some people learn a formula, others work backward from the angle-sum identity) to write that as a multiple of a shifted cosine.

But one formulaic approach is to use phasors. This may be, in effect, what @blamocur is suggesting.