Find the Exact Value sin(pi/6)cos(pi/6)-tan(pi/3)

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

Step 1

Simplify each term.

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

$\frac{1}{2} \cos (\frac{π}{6}) - \tan (\frac{π}{3})$

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

$\frac{1}{2} \cdot \frac{\sqrt{3}}{2} - \tan (\frac{π}{3})$

Multiply $\frac{1}{2} \cdot \frac{\sqrt{3}}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{\sqrt{3}}{2}$ .

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

Multiply $2$ by $2$ .

$\frac{\sqrt{3}}{4} - \tan (\frac{π}{3})$

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

$\frac{\sqrt{3}}{4} - \sqrt{3}$

Step 2

To write $- \sqrt{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{\sqrt{3}}{4} - \sqrt{3} \cdot \frac{4}{4}$

Step 3

Combine fractions.

Combine $- \sqrt{3}$ and $\frac{4}{4}$ .

$\frac{\sqrt{3}}{4} + \frac{- \sqrt{3} \cdot 4}{4}$

Combine the numerators over the common denominator.

$\frac{\sqrt{3} - \sqrt{3} \cdot 4}{4}$

Step 4

Simplify the numerator.

Multiply $4$ by $- 1$ .

$\frac{\sqrt{3} - 4 \sqrt{3}}{4}$

Subtract $4 \sqrt{3}$ from $\sqrt{3}$ .

$\frac{- 3 \sqrt{3}}{4}$

Step 5

Move the negative in front of the fraction.

$- \frac{3 \sqrt{3}}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{3 \sqrt{3}}{4}$

Decimal Form:

$- 1.29903810 \dots$