Find Period of Trig Functions

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.
 
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.
 
Jomo said:
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.
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Can you show me using the graph below? What is the period?

20200522_082611.jpg
 
Jomo said:
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.
Click to expand...

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
 
harpazo said:
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
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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.
 
harpazo said:
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
Click to expand...
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.
 
Harry_the_cat said:
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.
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I totally get it. Use the distance formula for points. Thanks.
 
Jomo said:
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.
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Very good. Thanks.
 
Graph two cycles of y = 3 sin x.

I know the first cycle ends at 2pi. Where does the second cycle end? How do I find the second cycle of the sine function?
 
Just add [MATH]2\pi[/MATH] for each cycle.

If each block in a city is 900 feet, then the first ends after 900, the second after 1800, the third after 2700, and so on. And in Trig City, every block looks exactly the same.
 
Dr.Peterson said:
Just add [MATH]2\pi[/MATH] for each cycle.

If each block in a city is 900 feet, then the first ends after 900, the second after 1800, the third after 2700, and so on. And in Trig City, every block looks exactly the same.
Click to expand...

Thanks. Will do.
 
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