# Find Period of Trig Functions

#### harpazo

##### Full Member
How do I find the period of a trig function from its graph?

#### Jomo

##### Elite Member
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
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
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?

#### harpazo

##### Full Member
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.

#### Harry_the_cat

##### Senior Member
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
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
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
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
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.