I want to find the period of the function
f
(
x
)
=
2
cos
conIjonnoraj0nls
Answered question
2022-06-03
I want to find the period of the function
which is a rational function of trig functions. So far I have found that: 1. the period of is ; 2. the period of is ; 3. the period of is ; 4. the period of is ; 5. and the period of is . How do I find the total period?
Answer & Explanation
amerce5acih
Beginner2022-06-04Added 1 answers
Each of the functions are periodic, each for different (since is a rational function of trig functions). You are missing a few, so I will fill in the full list: 1.For , , 2.For , , 3. For , , 4. For , , 5. For , , 6. For , . Then the question is what is the least common multiple of all of these numbers (Somos above said , I think you want ). Why the ? The least common multiple tells you what is the smallest number that is divisible by each of the above . That is because each of the functions will are periodic with the least common multiple. We want the smallest since if is periodic, it is also periodic. But we want the period . For the values listed above, the is 9. So the function is periodic. You can check this using your favorite software by checking as long as you avoid the x-values for which the function blows up.