Paridy and Codomain of Sine Function

There is no such thing as "paridy" but I think you mean "parity". That typically refers to something being "even" or "odd". A function is said to be "even" if f(-x)= f(x) or "odd" if f(-x)= -f(x).. f(x)= sin(x) is odd because sin(-x)= -sin(x). Of course most functions are "neither" even nor odd. It is even possible for a function to be both even and odd! For example, if f(x)=0 for all x then it is true that f(-x)= 0= f(x) and that f(-x)= 0= -f(x).

A function, f(x)= y, maps some set, X, to some set Y. The set of all x values is the "domain". The set of all y values, the results of applying f to all values in the domain, is the "co-domain". Since sin(x) lies between (and including) -1 and 1, the codomain is [-1, 1] which is a standard notation for "all numbers from -1 to 1 including -1 and 1".
 
HallsofIvy said:
There is no such thing as "paridy" but I think you mean "parity". That typically refers to something being "even" or "odd". A function is said to be "even" if f(-x)= f(x) or "odd" if f(-x)= -f(x).. f(x)= sin(x) is odd because sin(-x)= -sin(x). Of course most functions are "neither" even nor odd. It is even possible for a function to be both even and odd! For example, if f(x)=0 for all x then it is true that f(-x)= 0= f(x) and that f(-x)= 0= -f(x).

A function, f(x)= y, maps some set, X, to some set Y. The set of all x values is the "domain". The set of all y values, the results of applying f to all values in the domain, is the "co-domain". Since sin(x) lies between (and including) -1 and 1, the codomain is [-1, 1] which is a standard notation for "all numbers from -1 to 1 including -1 and 1".
Click to expand...

What you said about parity is not too clear for me. Can you define it another way?
 
Parity means whether something is even or odd. In the case of functions, this means symmetry across the y-axis or the origin.

Even and Odd Functions

A function is even when ... In other words there is symmetry about the y-axis (like a reflection)
www.mathsisfun.com

Does your book explain this?
 
Dr.Peterson said:
Parity means whether something is even or odd. In the case of functions, this means symmetry across the y-axis or the origin.

Even and Odd Functions

A function is even when ... In other words there is symmetry about the y-axis (like a reflection)
www.mathsisfun.com

Does your book explain this?
Click to expand...

I found this problem online. My textbooks are in storage until Friday.
 
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