Trigonometry Examples

$\sqrt{- 1 {(\frac{5}{6})}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $\frac{5}{6}$ .

$\sqrt{- 1 \frac{5^{2}}{6^{2}}}$

Step 1.2

Raise $5$ to the power of $2$ .

$\sqrt{- 1 \frac{25}{6^{2}}}$

Step 1.3

Raise $6$ to the power of $2$ .

$\sqrt{- 1 (\frac{25}{36})}$

Step 1.4

Rewrite $- 1 (\frac{25}{36})$ as $- (\frac{25}{36})$ .

$\sqrt{- \frac{25}{36}}$

Step 2

Rewrite $- \frac{25}{36}$ as ${(\frac{5 i}{6})}^{2}$ .

$\sqrt{{(\frac{5 i}{6})}^{2}}$

Step 3

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

$\frac{5 i}{6}$