What is the period of function g(t)?

[Ry122]

How do I find the period of this function?
g(t) = cos (4t) + sin (t)

 

[djeitnstine]

Graph it and check? Or would you rather do it by analysis.

 

[Ry122]

i need to do it without graphing

 

[HallsofIvy]

sin t is periodic with fundamental period $2\pi$ and cos 4t is periodic with fundamental period $\pi/2$. Since $2\pi= 4(\pi/2)$, $2\pi$ is also a period of cos 4t.