Sinx Period

C

curicuri

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May 30, 2019
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Hello if anyone has time I would appreciate if I could get som help!

Assignment
Determine A,k,v and d for the following Asin(kx-v) + d:
12375
My question
A=2
k=2
d=3

v??
My first thought was that v=15 since the curve is shifted 15 degrees backwards. This was apparently wrong. The correct answer is 60, which is calculated by the equation 2sin(2*75-v)=5. The equation I straight forward and I understand how to derive v from this.
Could someone help me to understand the reason why the answer is 60 and not 15, and if it is possible to derive 60 from graph direct without calculating it?

Thank you for time!
 
To answer the second question first, I find it easiest to read off the shift from a graph when it is written in factored form, y = Asin(k(x-u)) + d. (Here, your v is my ku. Do you see why?) In this form, u is the horizontal shift of the starting point of the curve, which is clearly 30° (because that is the value of x at which the curve crosses is center line). Therefore, v = ku = 2(30°) = 60°.

That, I think, also answers the first question. Can you explain more fully where you got 15°? If the basic function were -cos(x), I can see how you could say it was shifted 15° to the left (making v = -15); but it isn't. I'm guessing you just weren't clearly thinking about the sine.
 
I'll talk you through the process.
On the graph, look for the S shape of the basic sin x graph. Can you see that it starts at (30, 3)?
 
Thank your for the quick response.

Using your terminology really made it simple to deduce v, thanks to that I understand now how to deduce v!

Still I find it hard to determine that v=60 straight just by looking on the graph. Could you walk me through here? (if this is possible)
For your information, I understand after reading your replies that the phase shift is 30, and that a sinx function always "starts" at the center between its upward/downward shifts (sinx=0). Also do I understand the meaning of k, that k=2 speeds the period up by 2.
 
Note that you have used the form y = Asin(kx-v) + d while Dr P has used the form y = Asin(k(x-u)) + d.
Note the difference. In the second case, the sin "bit" is factorised. In the form you stated, it isn't.

u represents the phase shift, v doesn't.

So, using the other values you have correctly identified the function is:

y = 2 sin(2(x - 30o))+3
or
y = 2 sin (2x -60o) + 3 when the inner brackets are removed.

You can't directly determine v=60 from the graph. But you can determine u=30.

I'd suggest you use the factorised form and then expand out the sin "bit" if necessary. That's where the 60 comes from.
 
Perfect I note and understand what you say!
I now have got my questions answered, super thanks for helping me out ?
 
By the way, I can not find any tools for mathsymbols so one can write appropriate equations etcetera. Is there such a thing?
 
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