Theorem: TRIG.TID. The Trigonometric Identities for Supplementary Angles.

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

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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