# How do you determine if #F(x)= cos (sin x)# is an even or odd function?

A function

A function

Now we have that

Such functions have graphs that are symmetric about the y-axis as can be seen in the graph below

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To determine if the function (F(x) = \cos(\sin x)) is even or odd, we evaluate (F(-x)) and compare it with (F(x)).

- If (F(-x) = F(x)) for all (x) in the domain, the function is even.
- If (F(-x) = -F(x)) for all (x) in the domain, the function is odd.

Let's evaluate (F(-x)) and compare it with (F(x)):

[F(-x) = \cos(\sin(-x)) = \cos(-\sin x)]

Now, let's evaluate (F(x)):

[F(x) = \cos(\sin x)]

Since (\cos(-\theta) = \cos(\theta)) for all real numbers (\theta), if (F(-x) = F(x)) for all (x) in the domain, the function (F(x) = \cos(\sin x)) is even.

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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.

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.

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.

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