Trigonometry Examples

$- \frac{2 (\sqrt{- 84})}{6}$

Step 1

Rewrite $- 84$ as $- 1 (84)$ .

$- \frac{2 \sqrt{- 1 (84)}}{6}$

Step 2

Rewrite $\sqrt{- 1 (84)}$ as $\sqrt{- 1} \cdot \sqrt{84}$ .

$- \frac{2 (\sqrt{- 1} \cdot \sqrt{84})}{6}$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$- \frac{2 (i \cdot \sqrt{84})}{6}$

Step 4

Cancel the common factors.

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Step 4.1

Factor $2$ out of $6$ .

$- \frac{2 (i \cdot \sqrt{84})}{2 \cdot 3}$

Step 4.2

Cancel the common factor.

$- \frac{2 (i \cdot \sqrt{84})}{2 \cdot 3}$

Step 4.3

Rewrite the expression.

$- \frac{i \cdot \sqrt{84}}{3}$

$- \frac{i \cdot \sqrt{84}}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $84$ as $2^{2} \cdot 21$ .

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Step 5.1.1

Factor $4$ out of $84$ .

$- \frac{i \sqrt{4 (21)}}{3}$

Step 5.1.2

Rewrite $4$ as $2^{2}$ .

$- \frac{i \sqrt{2^{2} \cdot 21}}{3}$

$- \frac{i \sqrt{2^{2} \cdot 21}}{3}$

Step 5.2

Pull terms out from under the radical.

$- \frac{i \cdot 2 \sqrt{21}}{3}$

$- \frac{i \cdot 2 \sqrt{21}}{3}$

Step 6

Move $2$ to the left of $i$ .

$- \frac{2 i \sqrt{21}}{3}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$