Trigonometry Examples

$- \frac{1}{2} \cdot \sqrt{- 80}$

Step 1

Rewrite $- 80$ as $- 1 (80)$ .

$- \frac{1}{2} \cdot \sqrt{- 1 (80)}$

Step 2

Rewrite $\sqrt{- 1 (80)}$ as $\sqrt{- 1} \cdot \sqrt{80}$ .

$- \frac{1}{2} \cdot (\sqrt{- 1} \cdot \sqrt{80})$

Step 3

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

$- \frac{1}{2} \cdot (i \cdot \sqrt{80})$

Step 4

Rewrite $80$ as $4^{2} \cdot 5$ .

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Step 4.1

Factor $16$ out of $80$ .

$- \frac{1}{2} \cdot (i \cdot \sqrt{16 (5)})$

Step 4.2

Rewrite $16$ as $4^{2}$ .

$- \frac{1}{2} \cdot (i \cdot \sqrt{4^{2} \cdot 5})$

Step 5

Pull terms out from under the radical.

$- \frac{1}{2} \cdot (i \cdot (4 \sqrt{5}))$

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot (i \cdot (4 \sqrt{5}))$

Step 6.2

Factor $2$ out of $i \cdot (4 \sqrt{5})$ .

$\frac{- 1}{2} \cdot (2 (i \cdot (2 \sqrt{5})))$

Step 6.3

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 (i \cdot (2 \sqrt{5})))$

Step 6.4

Rewrite the expression.

$- 1 \cdot (i \cdot (2 \sqrt{5}))$

Step 7

Multiply $2$ by $- 1$ .

$- 2 i \sqrt{5}$