Trigonometry Examples

$\arctan (\frac{1}{\sqrt{3}})$

Step 1

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

$(\arctan (\frac{1}{\sqrt{3}})) \cdot \frac{180 °}{π}$

Step 2

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\arctan (\frac{1}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}) \cdot \frac{180}{π}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\arctan (\frac{\sqrt{3}}{\sqrt{3} \sqrt{3}}) \cdot \frac{180}{π}$

Step 3.2

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

$\arctan (\frac{\sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}) \cdot \frac{180}{π}$

Step 3.3

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

$\arctan (\frac{\sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}) \cdot \frac{180}{π}$

Step 3.4

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

$\arctan (\frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}}) \cdot \frac{180}{π}$

Step 3.5

Add $1$ and $1$ .

$\arctan (\frac{\sqrt{3}}{{\sqrt{3}}^{2}}) \cdot \frac{180}{π}$

Step 3.6

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

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Step 3.6.1

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

$\arctan (\frac{\sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}) \cdot \frac{180}{π}$

Step 3.6.2

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

$\arctan (\frac{\sqrt{3}}{3^{\frac{1}{2} \cdot 2}}) \cdot \frac{180}{π}$

Step 3.6.3

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

$\arctan (\frac{\sqrt{3}}{3^{\frac{2}{2}}}) \cdot \frac{180}{π}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$\arctan (\frac{\sqrt{3}}{3^{\frac{2}{2}}}) \cdot \frac{180}{π}$

Step 3.6.4.2

Rewrite the expression.

$\arctan (\frac{\sqrt{3}}{3^{1}}) \cdot \frac{180}{π}$

Step 3.6.5

Evaluate the exponent.

$\arctan (\frac{\sqrt{3}}{3}) \cdot \frac{180}{π}$

Step 4

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

$\frac{π}{6} \cdot \frac{180}{π}$

Step 5

Cancel the common factor of $π$ .

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Step 5.1

Cancel the common factor.

$\frac{π}{6} \cdot \frac{180}{π}$

Step 5.2

Rewrite the expression.

$\frac{1}{6} \cdot 180$

Step 6

Cancel the common factor of $6$ .

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Step 6.1

Factor $6$ out of $180$ .

$\frac{1}{6} \cdot (6 (30))$

Step 6.2

Cancel the common factor.

$\frac{1}{6} \cdot (6 \cdot 30)$

Step 6.3

Rewrite the expression.

$30$

Step 7

Convert to a decimal.

$30 °$