Trigonometry Examples

$\frac{5}{{(\frac{\sqrt{3}}{2})}^{2}}$

Step 1

Simplify the denominator.

Tap for more steps...

Step 1.1

Apply the product rule to $\frac{\sqrt{3}}{2}$ .

$\frac{5}{\frac{{\sqrt{3}}^{2}}{2^{2}}}$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$\frac{5}{\frac{{(3^{\frac{1}{2}})}^{2}}{2^{2}}}$

Step 1.2.2

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

$\frac{5}{\frac{3^{\frac{1}{2} \cdot 2}}{2^{2}}}$

Step 1.2.3

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

$\frac{5}{\frac{3^{\frac{2}{2}}}{2^{2}}}$

Step 1.2.4

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.2.4.1

Cancel the common factor.

$\frac{5}{\frac{3^{\frac{2}{2}}}{2^{2}}}$

Step 1.2.4.2

Rewrite the expression.

$\frac{5}{\frac{3^{1}}{2^{2}}}$

Step 1.2.5

Evaluate the exponent.

$\frac{5}{\frac{3}{2^{2}}}$

Step 1.3

Raise $2$ to the power of $2$ .

$\frac{5}{\frac{3}{4}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$5 (\frac{4}{3})$

Step 3

Multiply $5 (\frac{4}{3})$ .

Tap for more steps...

Step 3.1

Combine $5$ and $\frac{4}{3}$ .

$\frac{5 \cdot 4}{3}$

Step 3.2

Multiply $5$ by $4$ .

$\frac{20}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{20}{3}$

Decimal Form:

$6.\overline{6}$

Mixed Number Form:

$6 \frac{2}{3}$