Trigonometry Examples

\sqrt{- {(\sqrt{3})}^{2} + 1^{2}}

$\sqrt{- {(\sqrt{3})}^{2} + 1^{2}}$

Step 1

Rewrite

{\sqrt{3}}^{2}

${\sqrt{3}}^{2}$ as

3

$3$ .

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Step 1.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{3}

$\sqrt{3}$ as

3^{\frac{1}{2}}

$3^{\frac{1}{2}}$ .

\sqrt{- {(3^{\frac{1}{2}})}^{2} + 1^{2}}

$\sqrt{- {(3^{\frac{1}{2}})}^{2} + 1^{2}}$

Step 1.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\sqrt{- 3^{\frac{1}{2} \cdot 2} + 1^{2}}

$\sqrt{- 3^{\frac{1}{2} \cdot 2} + 1^{2}}$

Step 1.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

\sqrt{- 3^{\frac{2}{2}} + 1^{2}}

$\sqrt{- 3^{\frac{2}{2}} + 1^{2}}$

Step 1.4

Cancel the common factor of

2

$2$ .

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Step 1.4.1

Cancel the common factor.

\sqrt{- 3^{\frac{2}{2}} + 1^{2}}

$\sqrt{- 3^{\frac{2}{2}} + 1^{2}}$

Step 1.4.2

Rewrite the expression.

\sqrt{- 3^{1} + 1^{2}}

$\sqrt{- 3^{1} + 1^{2}}$

\sqrt{- 3^{1} + 1^{2}}

$\sqrt{- 3^{1} + 1^{2}}$

Step 1.5

Evaluate the exponent.

\sqrt{- 1 \cdot 3 + 1^{2}}

$\sqrt{- 1 \cdot 3 + 1^{2}}$

\sqrt{- 1 \cdot 3 + 1^{2}}

$\sqrt{- 1 \cdot 3 + 1^{2}}$

Step 2

Simplify the expression.

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Step 2.1

Multiply

- 1

$- 1$ by

3

$3$ .

\sqrt{- 3 + 1^{2}}

$\sqrt{- 3 + 1^{2}}$

Step 2.2

One to any power is one.

\sqrt{- 3 + 1}

$\sqrt{- 3 + 1}$

Step 2.3

Add

- 3

$- 3$ and

1

$1$ .

\sqrt{- 2}

$\sqrt{- 2}$

\sqrt{- 2}

$\sqrt{- 2}$

Step 3

Rewrite

- 2

$- 2$ as

- 1 (2)

$- 1 (2)$ .

\sqrt{- 1 (2)}

$\sqrt{- 1 (2)}$

Step 4

Rewrite

\sqrt{- 1 (2)}

$\sqrt{- 1 (2)}$ as

\sqrt{- 1} \cdot \sqrt{2}

$\sqrt{- 1} \cdot \sqrt{2}$ .

\sqrt{- 1} \cdot \sqrt{2}

$\sqrt{- 1} \cdot \sqrt{2}$

Step 5

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \sqrt{2}

$i \sqrt{2}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$