# Weird Trig Graph Question

"The period of function f is 5. If f(1)= 4, f(2)= 5, and f(4)= -2, what is the value of f(7)?"

I'm pretty sure this has something to do with function f(x) as a periodic function when a number p>0 exists, such that for all x in the domain of f, f(x + p) = f(x). I don't understand how this works. Maybe for the first one it sort of makes sense, but the rest of them don't follow the same pattern. I really appreciate any help I could get on this. Thanks.

## Answers and Replies

minger
Science Advisor
From what I can tell, it's a simple problem trying to get you to think about what a period is. Just think, what happens in one period of a repetitive function. Also another hint:
sin 0 = ?
sin 2pi = ?
sin 4pi = ?

FredGarvin
Science Advisor
Along the lines of what Minger said, think about what the definition of "period" is. It is the "time" it takes your function to complete 1 full cycle. So, if the period is 5, that means you can say it has 5 points in it and then it REPEATS. If points 1-5 are the first cycle and then it REPEATS, what can you say about point #7?