Expand the Trigonometric Expression sin(x-pi/3)

$\sin (x - \frac{π}{3})$

Apply the difference of angles identity.

$\sin (x) \cos (\frac{π}{3}) - \cos (x) \sin (\frac{π}{3})$

Simplify each term.

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$\sin (x) \frac{1}{2} - \cos (x) \sin (\frac{π}{3})$

Combine $\sin (x)$ and $\frac{1}{2}$ .

$\frac{\sin (x)}{2} - \cos (x) \sin (\frac{π}{3})$

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sin (x)}{2} - \cos (x) \frac{\sqrt{3}}{2}$

Combine $\frac{\sqrt{3}}{2}$ and $\cos (x)$ .

$\frac{\sin (x)}{2} - \frac{\sqrt{3} \cos (x)}{2}$