Trigonometry Examples

$\frac{34 (\frac{1}{2})}{\frac{\sqrt{3}}{2}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$34 (\frac{1}{2}) \frac{2}{\sqrt{3}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $34$ .

$2 (17) \frac{1}{2} \frac{2}{\sqrt{3}}$

Step 2.2

Cancel the common factor.

$2 \cdot 17 \frac{1}{2} \frac{2}{\sqrt{3}}$

Step 2.3

Rewrite the expression.

$17 \frac{2}{\sqrt{3}}$

Step 3

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

$17 (\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}})$

Step 4

Combine and simplify the denominator.

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Step 4.1

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

$17 \frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Step 4.2

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

$17 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Step 4.3

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

$17 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Step 4.4

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

$17 \frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Step 4.5

Add $1$ and $1$ .

$17 \frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}$

Step 4.6

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

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Step 4.6.1

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

$17 \frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Step 4.6.2

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

$17 \frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Step 4.6.3

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

$17 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 4.6.4

Cancel the common factor of $2$ .

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Step 4.6.4.1

Cancel the common factor.

$17 \frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Step 4.6.4.2

Rewrite the expression.

$17 \frac{2 \sqrt{3}}{3^{1}}$

Step 4.6.5

Evaluate the exponent.

$17 \frac{2 \sqrt{3}}{3}$

Step 5

Multiply $17 \frac{2 \sqrt{3}}{3}$ .

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Step 5.1

Combine $17$ and $\frac{2 \sqrt{3}}{3}$ .

$\frac{17 (2 \sqrt{3})}{3}$

Step 5.2

Multiply $2$ by $17$ .

$\frac{34 \sqrt{3}}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{34 \sqrt{3}}{3}$

Decimal Form:

$19.62990915 \dots$