Trigonometry Examples

$\frac{- 7}{\sqrt{- 49}}$

Step 1

Pull out imaginary unit $i$ .

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Step 1.1

Rewrite $- 49$ as $- 1 (49)$ .

$\frac{- 7}{\sqrt{- 1 (49)}}$

Step 1.2

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$\frac{- 7}{\sqrt{- 1} \cdot \sqrt{49}}$

Step 1.3

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

$\frac{- 7}{i \cdot \sqrt{49}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $49$ as $7^{2}$ .

$\frac{- 7}{i \sqrt{7^{2}}}$

Step 2.2

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

$\frac{- 7}{i \cdot 7}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Move $7$ to the left of $i$ .

$\frac{- 7}{7 i}$

Step 3.2

Cancel the common factor of $- 7$ and $7$ .

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Step 3.2.1

Factor $7$ out of $- 7$ .

$\frac{7 \cdot - 1}{7 i}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $7$ out of $7 i$ .

$\frac{7 \cdot - 1}{7 (i)}$

Step 3.2.2.2

Cancel the common factor.

$\frac{7 \cdot - 1}{7 i}$

Step 3.2.2.3

Rewrite the expression.

$\frac{- 1}{i}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{1}{i}$