Opposite real number identities(why $\cos(-x)=\cos x$) 
Ive been studying about opposite real number identities and Ive been stuck on this question on why $\cos(-x)=\cos x$.
Okay so if we consider that the given circle is a unit circle and triangle $pom$ and triangle $qom$ are congruent then how $\cos(-x)=\cos x$?
According to me when we will do base/hypotenuse for triangle qom then it will come $om/oq$ which should give $-\cos x$ as $oq$ is negative, right? 
Please help me through this.

Since you have already figured that $\triangle OMQ \cong \triangle OMP$, this means that the length of $OQ$ equals that of $OP$. In other words $|OQ|=|OP|$. Since they are congruent, their sides are equal in length and not opposite in sign.
Therefore by the identity
$$
\cos(\Theta)=\frac{\text{Adjacent}}{\text{Hypotenuse}},
$$
where the adjacent side might also be called the base. We have
$$
\cos(x)=\frac{|OM|}{|OP|},
$$
and
$$
\cos(-x)=\frac{|OM|}{|OQ|}=\frac{|OM|}{|OP|}=\cos(x).
$$
