How do I prove f is a periodic function with period 4π?

[chelseakerr]

My teacher never taught this so I have absolutely no idea what to do! If someone could please show step by step how to prove this, I would really appreaciate it!


Given: [FONT=MathJax_Math]f[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]cos[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT].[/FONT]
Prove: f is a periodic function with period 4π

 

[stapel]

My teacher never taught this so I have absolutely no idea what to do! If someone could please show step by step how to prove this, I would really appreaciate it!


Given: [FONT=MathJax_Math]f[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]cos[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT].[/FONT]
Prove: f is a periodic function with period 4π

Um... How are you studying trigonometry without the course ever having mentioned "periodic functions"? :shock:

 

[JeffM]

My teacher never taught this so I have absolutely no idea what to do! If someone could please show step by step how to prove this, I would really appreaciate it!


Given: [FONT=MathJax_Math]f[FONT=MathJax_Main]([/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]cos[/FONT][FONT=MathJax_Main]([/FONT][FONT=MathJax_Main]1[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main])[/FONT].[/FONT]
Prove: f is a periodic function with period 4π

What is the definition of a periodic function.

Is \(\displaystyle g( \theta ) = cos( \theta )\) a periodic function according to that definition? If so, what is its period?