[Math] Why is $\sin(x) = \sin(180^{\circ}-x)$

Question

I cannot seem to understand why this is true. Same for $\cos(x) = -\cos(180^{\circ}-x)$ and $\tan(x) = -\tan(180^{\circ}-x)$. Without the use of the compound angle formulas.

Thanks

Answer 1

Hint Rebember that $ \tan( 180^o \pm x ) = \frac{\sin( 180^o \pm x)}{\cos(180^o\pm x)}. $ Now draw the trigonometric cycle and observes the measures of sine and cosine.