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

Answer 1

Christian Antunez

See below

A function is even if #f(-x) = f(x)#. For example, #cos(-pi)=cospi#, so #y=cosx# is an even function.

A function is odd if #f(-x)=-f(x)#. For example, #sin(-pi)=-sinpi#, so #y=sinx# is an odd function.

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Answer 2

Greyson Brown

To determine if ( y = \cot(x) ) is an even or odd function, we need to analyze its symmetry properties.

An even function satisfies ( f(x) = f(-x) ) for all ( x ) in its domain. An odd function satisfies ( f(x) = -f(-x) ) for all ( x ) in its domain.

For ( y = \cot(x) ):

If ( y = \cot(x) ) is an even function, then ( \cot(x) = \cot(-x) ) for all ( x ) in its domain.
If ( y = \cot(x) ) is an odd function, then ( \cot(x) = -\cot(-x) ) for all ( x ) in its domain.

We know that ( \cot(-x) = \frac{\cos(-x)}{\sin(-x)} = \frac{\cos(x)}{-\sin(x)} = -\cot(x) ).

Since ( \cot(-x) = -\cot(x) ), ( y = \cot(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.