Find the Exact Value sin(pi/6)cos(pi/3)-tan(pi/4)

$\sin (\frac{π}{6}) \cos (\frac{π}{3}) - \tan (\frac{π}{4})$

Step 1

Simplify each term.

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

$\frac{1}{2} \cos (\frac{π}{3}) - \tan (\frac{π}{4})$

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

$\frac{1}{2} \cdot \frac{1}{2} - \tan (\frac{π}{4})$

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

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

$\frac{1}{2 \cdot 2} - \tan (\frac{π}{4})$

Multiply $2$ by $2$ .

$\frac{1}{4} - \tan (\frac{π}{4})$

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$\frac{1}{4} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$\frac{1}{4} - 1$

Step 2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{1}{4} - 1 \cdot \frac{4}{4}$

Step 3

Combine $- 1$ and $\frac{4}{4}$ .

$\frac{1}{4} + \frac{- 1 \cdot 4}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{1 - 1 \cdot 4}{4}$

Step 5

Simplify the numerator.

Multiply $- 1$ by $4$ .

$\frac{1 - 4}{4}$

Subtract $4$ from $1$ .

$\frac{- 3}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{3}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{3}{4}$

Decimal Form:

$- 0.75$