find domain in xy plane Watch

choccookies
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#1
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#1
function f(x,y)=log(xsiny)

find the domain in the xy-plane in which f(x,y) can be defined as a real-valued function. sketch this domain in the xy-plane in the region
-2pi < x< 2pi , -2pi < y <2pi.
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nota bene
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#2
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log(u) is real for u>0

0\le x\le2\pi combined with 0\le y\le\pi [edit: there is obviously the equivalent-2\pi\le y \le-\pi] gives real values, as does:
-2\pi\le x\le0 combined with -\pi\le y&lt;0 [edit: here there is the equivalent \pi\le y&lt;2\pi]also give real values. I think these are all combinations.

Does this help you?
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Notnek
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(Original post by nota bene)
log(u) is real for u>0

0\le x\le2\pi combined with 0\le y\le\pi [edit: there is obviously the equivalent-2\pi\le y \le-\pi] gives real values, as does:
-2\pi\le x\le0 combined with -\pi\le y&lt;0 [edit: here there is the equivalent \pi\le y&lt;2\pi]also give real values. I think these are all combinations.
The domain in the xy plane would be xsiny>0 though.
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nota bene
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(Original post by notnek)
The domain in the xy plane would be xsiny>0 though.
Yes, and that's surely what I've written:confused:

i.e. my first line reads: "let x vary between 0 and 2pi at the same time as letting y vary between 0 and pi OR y vary between -2pi and -pi."
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choccookies
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thats what i got for the domain, but how would i sketch this? in the region? what would the boundary lines be?
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Notnek
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(Original post by nota bene)
Yes, and that's surely what I've written:confused:

i.e. my first line reads: "let x vary between 0 and 2pi at the same time as letting y vary between 0 and pi OR y vary between -2pi and -pi."
Sorry it's just that i've already done this question and was just checking if my answers are correct.

I agree with you about the combinations.
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choccookies
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i still dont understand how to draw it including the boundary lines...
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Notnek
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(Original post by choccookies)
i still dont understand how to draw it including the boundary lines...
Nota bene told you the regions that you need to shade in your graph so I don't see your problem.
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choccookies
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sorry, this is the first time im trying a question like this,am i drawing the graph of xsiny and shading in the regions?
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