Trigonometry Examples

$\sqrt{- \frac{100}{225}}$

Step 1

Cancel the common factor of $100$ and $225$ .

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Step 1.1

Factor $25$ out of $100$ .

$\sqrt{- \frac{25 (4)}{225}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $25$ out of $225$ .

$\sqrt{- \frac{25 \cdot 4}{25 \cdot 9}}$

Step 1.2.2

Cancel the common factor.

$\sqrt{- \frac{25 \cdot 4}{25 \cdot 9}}$

Step 1.2.3

Rewrite the expression.

$\sqrt{- \frac{4}{9}}$

Step 2

Rewrite $- \frac{4}{9}$ as ${(\frac{2 i}{3})}^{2}$ .

$\sqrt{{(\frac{2 i}{3})}^{2}}$

Step 3

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

$\frac{2 i}{3}$