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

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Answer 1 · 2016-07-01T15:40:05

It is neither.

To be even the function must obey:

$f (- x) = f (x)$ $f(-x) = f(x)$

To be odd, the function must obey:

$f (- x) = - f (x)$ $f(-x) = -f(x)$

In this case,

$F (- x) = sin (- x) + cos (- x) = - sin (x) + cos (x)$ $F(-x) = sin(-x) + cos(-x) = -sin(x) + cos(x)$

$F (- x) \neq F (x) or - F (x)$ $F(-x) != F(x) or -F(x)$ hence it is neither even or odd.

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