Find Period of Trig Functions

harpazo

Full Member
Joined
Jan 31, 2013
Messages
783
How do I find the period of a trig function from its graph?
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
7,035
You set the angle to 0 and set the angle to 2pi. Solve for the variable in each case. Compute the absolute value of the difference between those numbers.
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
7,035
Oh, from the graph. You find one full period of the graph and subtract the x-valus from the start and finish of that period. Take the absolute value of that difference.
 

harpazo

Full Member
Joined
Jan 31, 2013
Messages
783
You set the angle to 0 and set the angle to 2pi. Solve for the variable in each case. Compute the absolute value of the difference between those numbers.
Can you show me using the graph below? What is the period?

20200522_082611.jpg
 

harpazo

Full Member
Joined
Jan 31, 2013
Messages
783
Oh, from the graph. You find one full period of the graph and subtract the x-valus from the start and finish of that period. Take the absolute value of that difference.
Can you please show me what you mean using the graph below. I will then return to the textbook to solve similar problems following your steps here.

20200522_082619.jpg
 

Harry_the_cat

Senior Member
Joined
Mar 16, 2016
Messages
1,951
Can you show me using the graph below? What is the period?

View attachment 19114
See (0,0) is on the graph. After one full cycle, or S shape, we get to the point (2pi,0).
What distance is that on the x-axis? 2pi. So the period is 2pi.
 

Harry_the_cat

Senior Member
Joined
Mar 16, 2016
Messages
1,951
Can you please show me what you mean using the graph below. I will then return to the textbook to solve similar problems following your steps here.

View attachment 19115
On this one, I'd look at (0, 3) and (8, 3). That's a full cycle so period is 8.
It doesnt matter what two points you look at, as long as there is a full cycle between them. For example, (4, -3) and (12,-3). Period is still 8.
 

Jomo

Elite Member
Joined
Dec 30, 2014
Messages
7,035
Can you please show me what you mean using the graph below. I will then return to the textbook to solve similar problems following your steps here.

View attachment 19115
One period starts at 0 and finishes at 8. Another period/cycle starts at 4 and finishes at 12. Another one starts at starts at -4 and finishes at 4. Just take any of those and subtract the end values. For example 8-0 = 8, 12-4 = 8, 4-(-4) = 8. The length of the period is 8.
 

harpazo

Full Member
Joined
Jan 31, 2013
Messages
783
See (0,0) is on the graph. After one full cycle, or S shape, we get to the point (2pi,0).
What distance is that on the x-axis? 2pi. So the period is 2pi.
I totally get it. Use the distance formula for points. Thanks.
 

harpazo

Full Member
Joined
Jan 31, 2013
Messages
783
One period starts at 0 and finishes at 8. Another period/cycle starts at 4 and finishes at 12. Another one starts at starts at -4 and finishes at 4. Just take any of those and subtract the end values. For example 8-0 = 8, 12-4 = 8, 4-(-4) = 8. The length of the period is 8.
Very good. Thanks.
 
Top