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How do you determine if #y=sin x# is an even or odd function?

Answer 1

Elijah Allen

see below

definitions

#f(-x)=f(x)=>f(x)" is even"#

#f(-x)=-f(x)=>f(x)" is odd"#

#f(x)=sinx#

#f(-x)=sin(-x)=-sinx#

#:.sinx" is odd"#

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Answer 2

Madelyn Anderson

To determine if ( y = \sin(x) ) is an even or odd function, you can evaluate the function at negative ( x ) values and see if it satisfies the properties of even or odd functions.

Even function: A function ( f(x) ) is even if ( f(-x) = f(x) ) for all ( x ) in the domain. This means that the graph of an even function is symmetric about the y-axis.
Odd function: A function ( f(x) ) is odd if ( f(-x) = -f(x) ) for all ( x ) in the domain. This means that the graph of an odd function is symmetric about the origin.

For the function ( y = \sin(x) ):

Evaluating ( \sin(-x) ), we get ( \sin(-x) = -\sin(x) ).

Since ( \sin(-x) = -\sin(x) ), the function ( y = \sin(x) ) satisfies the property of an odd function.

Therefore, ( y = \sin(x) ) is an odd function.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.