Theorem:TRIG.SYM. Symmetry of The Core Trigonometric Functions

• $\cos(-x)= \cos(x)$ for all $x$. The cosine function has even symmetry with respect to $x=0$.
• $\sin(-x)= -\sin(x)$ for all $x$. The sine function has odd symmetry with respect to $(0,0)$.
• $\tan(-x)= -\tan(x)$ for all $x \ne \frac {(2k+1)\pi}2$. The tangent function has odd symmetry with respect to $(0,0)$.
  

The justification for these symmetries can be understood by considering the mapping diagrams for the unit circle definitions of these functions as well as visualized with their graphs

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