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

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

Step 1

Simplify each term.

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

$\frac{\sqrt{3}}{2} \cos (\frac{π}{6}) - \tan (\frac{π}{4})$

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

$\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} - \tan (\frac{π}{4})$

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

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

$\frac{\sqrt{3} \sqrt{3}}{2 \cdot 2} - \tan (\frac{π}{4})$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{{\sqrt{3}}^{1} \sqrt{3}}{2 \cdot 2} - \tan (\frac{π}{4})$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}{2 \cdot 2} - \tan (\frac{π}{4})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{{\sqrt{3}}^{1 + 1}}{2 \cdot 2} - \tan (\frac{π}{4})$

Add $1$ and $1$ .

$\frac{{\sqrt{3}}^{2}}{2 \cdot 2} - \tan (\frac{π}{4})$

Multiply $2$ by $2$ .

$\frac{{\sqrt{3}}^{2}}{4} - \tan (\frac{π}{4})$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$\frac{3}{4} - \tan (\frac{π}{4})$

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

$\frac{3}{4} - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$\frac{3}{4} - 1$

Step 2

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

$\frac{3}{4} - 1 \cdot \frac{4}{4}$

Step 3

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

$\frac{3}{4} + \frac{- 1 \cdot 4}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{3 - 1 \cdot 4}{4}$

Step 5

Simplify the numerator.

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $3$ .

$\frac{- 1}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{1}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{4}$

Decimal Form:

$- 0.25$

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

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