Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $- \sqrt{3}$ .

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

Step 1.2

Raise $- 1$ to the power of $2$ .

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

Step 1.3

Multiply ${\sqrt{3}}^{2}$ by $1$ .

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

Step 1.4

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

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Step 1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 1.4.2

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

$v (3^{\frac{1}{2} \cdot 2} + {(1)}^{2})$

Step 1.4.3

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

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

Step 1.4.4

Cancel the common factor of $2$ .

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Step 1.4.4.1

Cancel the common factor.

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

Step 1.4.4.2

Rewrite the expression.

$v (3^{1} + {(1)}^{2})$

Step 1.4.5

Evaluate the exponent.

$v (3 + {(1)}^{2})$

Step 1.5

One to any power is one.

$v (3 + 1)$

Step 2

Simplify the expression.

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Step 2.1

Add $3$ and $1$ .

$v \cdot 4$

Step 2.2

Move $4$ to the left of $v$ .

$4 v$