Trigonometry Examples

$\cos (\frac{π}{6} - x)$

Step 1

Apply the difference of angles identity $\cos (x - y) = \cos (x) \cos (y) + \sin (x) \sin (y)$ .

$\cos (\frac{π}{6}) \cos (x) + \sin (\frac{π}{6}) \sin (x)$

Step 2

Simplify each term.

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Step 2.1

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$\frac{\sqrt{3}}{2} \cos (x) + \sin (\frac{π}{6}) \sin (x)$

Step 2.2

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

$\frac{\sqrt{3} \cos (x)}{2} + \sin (\frac{π}{6}) \sin (x)$

Step 2.3

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

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

Step 2.4

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

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