Trigonometry Examples

$v ({(2 - 0)}^{2} + {(2 \sqrt{3 - 0})}^{2})$

Step 1

Simplify each term.

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Step 1.1

Subtract $0$ from $2$ .

$v (2^{2} + {(2 \sqrt{3 - 0})}^{2})$

Step 1.2

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

$v (4 + {(2 \sqrt{3 - 0})}^{2})$

Step 1.3

Multiply $- 1$ by $0$ .

$v (4 + {(2 \sqrt{3 + 0})}^{2})$

Step 1.4

Add $3$ and $0$ .

$v (4 + {(2 \sqrt{3})}^{2})$

Step 1.5

Apply the product rule to $2 \sqrt{3}$ .

$v (4 + 2^{2} {\sqrt{3}}^{2})$

Step 1.6

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

$v (4 + 4 {\sqrt{3}}^{2})$

Step 1.7

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

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Step 1.7.1

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

$v (4 + 4 {(3^{\frac{1}{2}})}^{2})$

Step 1.7.2

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

$v (4 + 4 \cdot 3^{\frac{1}{2} \cdot 2})$

Step 1.7.3

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

$v (4 + 4 \cdot 3^{\frac{2}{2}})$

Step 1.7.4

Cancel the common factor of $2$ .

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Step 1.7.4.1

Cancel the common factor.

$v (4 + 4 \cdot 3^{\frac{2}{2}})$

Step 1.7.4.2

Rewrite the expression.

$v (4 + 4 \cdot 3^{1})$

Step 1.7.5

Evaluate the exponent.

$v (4 + 4 \cdot 3)$

Step 1.8

Multiply $4$ by $3$ .

$v (4 + 12)$

Step 2

Simplify the expression.

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Step 2.1

Add $4$ and $12$ .

$v \cdot 16$

Step 2.2

Move $16$ to the left of $v$ .

$16 v$