Interference of 3 Cosine Waves: Can They Cancel Out?

[grooveactiva]

Homework Statement

3 waves are represented by these 3 waves inteferring:
cos(Θ-π), cos(Θ+π), 3cos(Θ)?
cos($$\theta$$-$$\pi$$), cos($$\theta$$+$$\pi$$), 3cos($$\theta$$).

If I want to diagram these, does the cos($$\theta$$-$$\pi$$) and cos($$\theta$$+$$\pi$$), cancel each other out?

Do I need to convert them to sine functions or can I leave them cosine functions?

Homework Equations

cos(Θ-π), cos(Θ+π), 3cos(Θ).
cos($$\theta$$-$$\pi$$), cos($$\theta$$+$$\pi$$), 3cos($$\theta$$).

The Attempt at a Solution

 

[lanedance]

can you use complex exponentials, and is there any time dependence?