Trigonometry Examples

$\frac{\sqrt{- 36}}{- \sqrt{4}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 36$ as $- 1 (36)$ .

$\frac{\sqrt{- 1 (36)}}{- \sqrt{4}}$

Step 1.2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{36}}{- \sqrt{4}}$

Step 1.3

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

$\frac{i \cdot \sqrt{36}}{- \sqrt{4}}$

Step 2

Combine $\sqrt{36}$ and $\sqrt{4}$ into a single radical.

$\frac{i \cdot \sqrt{\frac{36}{4}}}{- 1}$

Step 3

Cancel the common factor of $36$ and $4$ .

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Step 3.1

Factor $4$ out of $36$ .

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4}}}{- 1}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $4$ .

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4 (1)}}}{- 1}$

Step 3.2.2

Cancel the common factor.

$\frac{i \cdot \sqrt{\frac{4 \cdot 9}{4 \cdot 1}}}{- 1}$

Step 3.2.3

Rewrite the expression.

$\frac{i \cdot \sqrt{\frac{9}{1}}}{- 1}$

Step 3.2.4

Divide $9$ by $1$ .

$\frac{i \cdot \sqrt{9}}{- 1}$

Step 4

Simplify the expression.

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Step 4.1

Move the negative one from the denominator of $\frac{i \cdot \sqrt{9}}{- 1}$ .

$- 1 \cdot (i \cdot \sqrt{9})$

Step 4.2

Rewrite $- 1 \cdot (i \cdot \sqrt{9})$ as $- (i \cdot \sqrt{9})$ .

$- (i \cdot \sqrt{9})$

Step 4.3

Rewrite $9$ as $3^{2}$ .

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

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$- (i \cdot 3)$

Step 6

Move $3$ to the left of $i$ .

$- (3 \cdot i)$

Step 7

Multiply $3$ by $- 1$ .

$- 3 i$