Trigonometry Examples

$\frac{7}{\sqrt{9 - 49}}$

Step 1

Simplify the denominator.

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Step 1.1

Subtract $49$ from $9$ .

$\frac{7}{\sqrt{- 40}}$

Step 1.2

Rewrite $- 40$ as $- 1 (40)$ .

$\frac{7}{\sqrt{- 1 (40)}}$

Step 1.3

Rewrite $\sqrt{- 1 (40)}$ as $\sqrt{- 1} \cdot \sqrt{40}$ .

$\frac{7}{\sqrt{- 1} \cdot \sqrt{40}}$

Step 1.4

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

$\frac{7}{i \cdot \sqrt{40}}$

Step 1.5

Rewrite $40$ as $2^{2} \cdot 10$ .

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Step 1.5.1

Factor $4$ out of $40$ .

$\frac{7}{i \cdot \sqrt{4 (10)}}$

Step 1.5.2

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

$\frac{7}{i \cdot \sqrt{2^{2} \cdot 10}}$

Step 1.6

Pull terms out from under the radical.

$\frac{7}{i \cdot (2 \sqrt{10})}$

Step 1.7

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

$\frac{7}{2 i \sqrt{10}}$

Step 2

Multiply $\frac{7}{2 i \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{7}{2 i \sqrt{10}} \cdot \frac{\sqrt{10}}{\sqrt{10}}$

Step 3

Combine and simplify the denominator.

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Step 3.1

Multiply $\frac{7}{2 i \sqrt{10}}$ by $\frac{\sqrt{10}}{\sqrt{10}}$ .

$\frac{7 \sqrt{10}}{2 i \sqrt{10} \sqrt{10}}$

Step 3.2

Move $\sqrt{10}$ .

$\frac{7 \sqrt{10}}{2 i (\sqrt{10} \sqrt{10})}$

Step 3.3

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{7 \sqrt{10}}{2 i ({\sqrt{10}}^{1} \sqrt{10})}$

Step 3.4

Raise $\sqrt{10}$ to the power of $1$ .

$\frac{7 \sqrt{10}}{2 i ({\sqrt{10}}^{1} {\sqrt{10}}^{1})}$

Step 3.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{7 \sqrt{10}}{2 i {\sqrt{10}}^{1 + 1}}$

Step 3.6

Add $1$ and $1$ .

$\frac{7 \sqrt{10}}{2 i {\sqrt{10}}^{2}}$

Step 3.7

Rewrite ${\sqrt{10}}^{2}$ as $10$ .

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Step 3.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{10}$ as $10^{\frac{1}{2}}$ .

$\frac{7 \sqrt{10}}{2 i {(10^{\frac{1}{2}})}^{2}}$

Step 3.7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{7 \sqrt{10}}{2 i \cdot 10^{\frac{1}{2} \cdot 2}}$

Step 3.7.3

Combine $\frac{1}{2}$ and $2$ .

$\frac{7 \sqrt{10}}{2 i \cdot 10^{\frac{2}{2}}}$

Step 3.7.4

Cancel the common factor of $2$ .

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Step 3.7.4.1

Cancel the common factor.

$\frac{7 \sqrt{10}}{2 i \cdot 10^{\frac{2}{2}}}$

Step 3.7.4.2

Rewrite the expression.

$\frac{7 \sqrt{10}}{2 i \cdot 10^{1}}$

Step 3.7.5

Evaluate the exponent.

$\frac{7 \sqrt{10}}{2 i \cdot 10}$

Step 4

Multiply $10$ by $2$ .

$\frac{7 \sqrt{10}}{20 i}$