# Is the trig function: even, odd, neither y=cosx?

It is even since $\cos \left(- x\right) = \cos x \forall x \in \mathbb{R}$
By definition, $f$ is an odd function if $f \left(- x\right) = - f \left(x\right)$
$f$ is an even function if $f \left(- x\right) = f \left(x\right)$
Since $\cos \left(- x\right) = \cos x$ for all $x \in \mathbb{R}$, it implies that $f \left(x\right) = \cos x$ is an even function.