What is the domain of f ( x , y ) </mrow> = arctan &#x2

xonycutieoxl1

xonycutieoxl1

Answered question

2022-06-14

What is the domain of f ( x , y ) = arctan ( 1 sin ( x + y ) )

Answer & Explanation

Amy Daniels

Amy Daniels

Beginner2022-06-15Added 20 answers

arctan 's domain is all of R . So you only need worry about when 1 sin ( x + y ) is undefined. So the domain is
{ ( x , y ) : sin ( x + y ) 0 }
More explicitly, this is
{ ( x , y ) : x + y π Z }
The way I have written it, x + y π must fall in between two consecutive integers.
Your domain, looking with n=0, allows x=−1, y=1. Which is clearly not in the domain
cazinskup3

cazinskup3

Beginner2022-06-16Added 6 answers

It's not exactly that:
sin ( x + y ) 0 x + y 0 mod π
i. e. x + y n π ( n Z ). So you have to remove a family of lines parallel to the second bissectrix.

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