Precalculus Examples

$\sin (\frac{π}{3} - x)$

Step 1

Apply the difference of angles identity.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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