Is the Highlighted Portion a Mistake and Where Does the PI Go?

[Turion]

The highlighted in yellow is a mistake, right? I might be going insane.

Where does the PI go?

 

[Office_Shredder]

$$\cos(4(t+\pi)) = \cos(4t+4\pi) = \cos(4t)$$

 

[SteamKing]

Remember, sin and cos are periodic functions with period 2k*pi, k = integer.

 

[Turion]

@Office_Shredder: Opps. Nice catch.

@SteamKing: Isn't the period 2pi/k where k is the coefficient of t?