# 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.

#### 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.

• harpazo

#### 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

#### 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.