Find the Exact Value sin(30)cos(60)+sin(60)cos(30)

$\sin (30) \cos (60) + \sin (60) \cos (30)$

Simplify each term.

The exact value of $\sin (30)$ is $\frac{1}{2}$ .

$\frac{1}{2} \cos (60) + \sin (60) \cos (30)$

The exact value of $\cos (60)$ is $\frac{1}{2}$ .

$\frac{1}{2} \cdot \frac{1}{2} + \sin (60) \cos (30)$

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

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

$\frac{1}{2 \cdot 2} + \sin (60) \cos (30)$

Multiply $2$ by $2$ .

$\frac{1}{4} + \sin (60) \cos (30)$

The exact value of $\sin (60)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{1}{4} + \frac{\sqrt{3}}{2} \cos (30)$

The exact value of $\cos (30)$ is $\frac{\sqrt{3}}{2}$ .

$\frac{1}{4} + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2}$

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

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

$\frac{1}{4} + \frac{\sqrt{3} \sqrt{3}}{2 \cdot 2}$

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

$\frac{1}{4} + \frac{{\sqrt{3}}^{1} \sqrt{3}}{2 \cdot 2}$

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

$\frac{1}{4} + \frac{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}{2 \cdot 2}$

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

$\frac{1}{4} + \frac{{\sqrt{3}}^{1 + 1}}{2 \cdot 2}$

Add $1$ and $1$ .

$\frac{1}{4} + \frac{{\sqrt{3}}^{2}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$\frac{1}{4} + \frac{{\sqrt{3}}^{2}}{4}$

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

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

$\frac{1}{4} + \frac{{(3^{\frac{1}{2}})}^{2}}{4}$

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

$\frac{1}{4} + \frac{3^{\frac{1}{2} \cdot 2}}{4}$

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

$\frac{1}{4} + \frac{3^{\frac{2}{2}}}{4}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{1}{4} + \frac{3^{\frac{2}{2}}}{4}$

Rewrite the expression.

$\frac{1}{4} + \frac{3^{1}}{4}$

Evaluate the exponent.

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

Combine fractions.

Combine the numerators over the common denominator.

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

Simplify the expression.

Add $1$ and $3$ .

$\frac{4}{4}$

Divide $4$ by $4$ .

$1$

Find the Exact Value sin(30)cos(60)+sin(60)cos(30)

Related Questions

Support LCMGCF.com by disabling your adblocker.