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Maths question ---- Unit circle.


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A really quite question.

If 

 

s = 2 sin( pi * t ) + sin (2 * pi * t ), t is bigger or equals to 0.

 

When is the period of the function s?

 and why?

 

I'm not really sure what the best way is to explain this question. I suspect there must be a way to re-write function 's' into the standard form (from which we can derive the period); however, I haven't found it yet. But anyway, I'll to explain this the best I can using words:

 

It's clear that 's' is just the superposition of 2 separate functions, gif.latex? \sin\left(\pi t\right) and gif.latex? \sin\left(2\pi t\right) (we will forget about the number '2' in front of the sine, because the amplitude doesn't play a role in finding the period). In other words, if you put the graphs of these 2 functions on top of one another, and then superpose them, you'll get the function 's'.

 

Now, it's pretty obvious that function gif.latex? \sin\left(\pi t\right) has the period of 2, and function gif.latex? \sin\left(2\pi t\right) has the period of 1. Notice that these 2 periods are multiples of each other. So by the time gif.latex? \sin\left(\pi t\right)has finished one period, gif.latex? \sin\left(2\pi t\right)has done 2 periods. And by that time, they will repeat this process once again. Hence, the period of function 's' is nothing more than the period of the function gif.latex? \sin\left(\pi t\right) itself.

 

Conclusion, 's' has the period of 2. I've already checked this with the calculator. Feel free to ask if you have further questions :)

Edited by Vioh
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A really quite question.

If 

 

s = 2 sin( pi * t ) + sin (2 * pi * t ), t is bigger or equals to 0.

 

When is the period of the function s?

 and why?

 

I'm not really sure what the best way is to explain this question. I suspect there must be a way to re-write function 's' into the standard form (from which we can derive the period); however, I haven't found it yet. But anyway, I'll to explain this the best I can using words:

 

It's clear that 's' is just the superposition of 2 separate functions, gif.latex? \sin\left(\pi t\right) and gif.latex? \sin\left(2\pi t\right) (we will forget about the number '2' in front of the sine, because the amplitude doesn't play a role in finding the period). In other words, if you put the graphs of these 2 functions on top of one another, and then superpose them, you'll get the function 's'.

 

Now, it's pretty obvious that function gif.latex? \sin\left(\pi t\right) has the period of 2, and function gif.latex? \sin\left(2\pi t\right) has the period of 1. Notice that these 2 periods are multiples of each other. So by the time gif.latex? \sin\left(\pi t\right)has finished one period, gif.latex? \sin\left(2\pi t\right)has done 2 periods. And by that time, they will repeat this process once again. Hence, the period of function 's' is nothing more than the period of the function gif.latex? \sin\left(\pi t\right) itself.

 

Conclusion, 's' has the period of 2. I've already checked this with the calculator. Feel free to ask if you have further questions :)

 

I might need some time to digest it. Haha . BUT thank you so so much.

Edited by Guest
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