Question

Can someone please explain how to find the period of a function from just a given sine or cosine graph.

Answer 1

look to see the length of the interval over which the function completes all it does

Answer 2

maybe look at the length from top to top, or bottom to bottom

Answer 3

Here is an example of the graph that I have to find the equation to. I have that the amplitude is 1, but how do I find the period?

Answer 4

See it completes one cycle from 0 to 2. The second cycle would be from 2 to 4

Answer 5

it does everything over the interval \([0,2]\) therefore the period is 2

Answer 6

here is an example of a sine curve with period 1
https://www.wolframalpha.com/input/?i=sin%282+pi+x%29

Answer 7

Ohh!! The lightbulb just went off! Lol!! So for the equation you would have to divide 2pi by 2. right?

Answer 8

here is one with period 4
https://www.wolframalpha.com/input/?i=sin%28pi+x%2F2%29

Answer 9

if you want the equation for the function, know that \(\sin(bx)\) has period \(\frac{2\pi}{b}\)
since you know the period is 2, set
\[\frac{2\pi}{b}=2\] and solve for \(b\)

Answer 10

Okay! Thank you so much! I get it now. Does this also apply to cosine graphs?

Answer 11

For this graph would you also do \[\frac{ 2\pi }{ b }=2\] and solve for b?

Answer 12

this is also a sine graph, since it goes right through the origin.
but the period is not 2 in this case

Answer 13

How are you supposed to determine the period then?

Answer 14

to answer your earlier question, yes you would set
\[\frac{2\pi}{b}=2\] and solve for \(b\)

Answer 15

you get \(b=\pi\) so your graph for the first one (not the second one) would be
\[y=\sin(\pi x)\]

Answer 16

Okay, I understand that, but for the second graph that I posted, how would you dtermine the period? In the textbook the answer is y=sin2x, but I dont know how to get there.

Answer 17

for the second one, determine the period pretty much with your eyeballs
starts at \(0\) then goes up ot \(1\)
then goes back down to to 0, then further down to \(-1\) and then back up to \(0\) all in an interval of length \(\pi\)

Answer 18

Yayay!! Omg thank you soooo much!!! I really understand this now and just got the next 5 homework questions right!! Thanks a billion!!! :D