Basic Math Examples

arctan (\frac{5}{- 5 \sqrt{3}})

$\arctan (\frac{5}{- 5 \sqrt{3}})$

Step 1

Cancel the common factor of

5

$5$ and

- 5

$- 5$ .

Tap for more steps...

Step 1.1

Factor

5

$5$ out of

5

$5$ .

arctan (\frac{5 (1)}{- 5 \sqrt{3}})

$\arctan (\frac{5 (1)}{- 5 \sqrt{3}})$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor

5

$5$ out of

- 5 \sqrt{3}

$- 5 \sqrt{3}$ .

arctan ⎛ ⎜ ⎝ \frac{5 (1)}{5 (- \sqrt{3})} ⎞ ⎟ ⎠

$\arctan (\frac{5 (1)}{5 (- \sqrt{3})})$

Step 1.2.2

Cancel the common factor.

$\arctan (\frac{5 \cdot 1}{5 (- \sqrt{3})})$

Step 1.2.3

Rewrite the expression.

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

Step 2

Cancel the common factor of

$1$ and

$- 1$ .

Tap for more steps...

Step 2.1

Rewrite

$1$ as

$- 1 (- 1)$ .

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

Step 2.2

Move the negative in front of the fraction.

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

Step 3

Multiply

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

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 4

Combine and simplify the denominator.

Tap for more steps...

Step 4.1

Multiply

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

$\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Step 4.2

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 4.3

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 4.4

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\arctan (- \frac{\sqrt{3}}{{\sqrt{3}}^{1 + 1}})$

Step 4.5

Add

$1$ and

$1$ .

$\arctan (- \frac{\sqrt{3}}{{\sqrt{3}}^{2}})$

Step 4.6

Rewrite

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

$3$ .

Tap for more steps...

Step 4.6.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{3}$ as

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

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

Step 4.6.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.6.3

Combine

$\frac{1}{2}$ and

$2$ .

$\arctan (- \frac{\sqrt{3}}{3^{\frac{2}{2}}})$

Step 4.6.4

Cancel the common factor of

$2$ .

Tap for more steps...

Step 4.6.4.1

Cancel the common factor.

$\arctan (- \frac{\sqrt{3}}{3^{\frac{2}{2}}})$

Step 4.6.4.2

Rewrite the expression.

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

Step 4.6.5

Evaluate the exponent.

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

Step 5

The exact value of

$\arctan (- \frac{\sqrt{3}}{3})$ is

$- \frac{π}{6}$ .

$- \frac{π}{6}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{π}{6}$

Decimal Form:

$- 0.52359877 \dots$