Trigonometry Examples

$\tan (\frac{π}{6} - \sin (\frac{π}{3}))$

Step 1

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

$\tan (\frac{π}{6} - \frac{\sqrt{3}}{2})$

Step 2

Rewrite $\tan (\frac{π}{6} - \frac{\sqrt{3}}{2})$ in terms of sines and cosines.

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

Step 3

Convert from $\frac{\sin (\frac{π}{6} - \frac{\sqrt{3}}{2})}{\cos (\frac{π}{6} - \frac{\sqrt{3}}{2})}$ to $\tan (\frac{π}{6} - \frac{\sqrt{3}}{2})$ .

$\tan (\frac{π}{6} - \frac{\sqrt{3}}{2})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\tan (\frac{π}{6} - \frac{\sqrt{3}}{2})$

Decimal Form:

$- 0.35646950 \dots$