Trigonometry Examples

$f (- 6) = \sqrt{r + 6 - 4}$

Step 1

Replace the variable $r$ with $- 6$ in the expression.

$f (- 6) = \sqrt{(- 6) + 6 - 4}$

Step 2

Simplify the result.

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Step 2.1

Simplify by adding numbers.

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Step 2.1.1

Add $- 6$ and $6$ .

$f (- 6) = \sqrt{0 - 4}$

Step 2.1.2

Subtract $4$ from $0$ .

$f (- 6) = \sqrt{- 4}$

Step 2.2

Rewrite $- 4$ as $- 1 (4)$ .

$f (- 6) = \sqrt{- 1 \cdot 4}$

Step 2.3

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$f (- 6) = \sqrt{- 1} \cdot \sqrt{4}$

Step 2.4

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

$f (- 6) = i \cdot \sqrt{4}$

Step 2.5

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

$f (- 6) = i \cdot \sqrt{2^{2}}$

Step 2.6

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

$f (- 6) = i \cdot 2$

Step 2.7

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

$f (- 6) = 2 i$

Step 2.8

The final answer is $2 i$ .

$2 i$

Step 3