Trigonometry Examples

$\sin (x + \frac{π}{6})$

Step 1

Apply the sum of angles identity.

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

Step 2

Simplify each term.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

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

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