The sine function has symmetry:
$$\sin(\pi - \theta) = \sin(\theta)$$
This relationship is derived from the fact that the sine function is even about the line $x = \frac \pi2 $ graphically.
This means that
$$\sin(\frac{\pi}{2}-u)=\sin(\frac{\pi}{2}+u)$$
For all $u \in \mathbb{R}$
Using the substitution $u = x - \frac{\pi}{2}$:
$$\sin(\frac{\pi}{2} - (x - \frac{\pi}{2}))=\sin(\frac{\pi}{2}+ x - \frac{\pi}{2})$$
$$\sin(\pi - x)=\sin(x)$$
For instance, $\sin(60^\circ)=\sin(120^\circ)$ because $120^\circ=180^\circ-60^\circ$.
This symmetry property of sine is related to its odd function nature, where $\sin(-\theta) = -\sin(\theta)$.
The cosine function has a similar symmetry property:
$$\cos(\pi - \theta) = -\cos(\theta)$$
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