Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Raise

$- 2$ to the power of

$2$ .

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

Step 1.2

Apply the product rule to

$- 2 \sqrt{3}$ .

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

Step 1.3

Raise

$- 2$ to the power of

$2$ .

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

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

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

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

Step 1.4.2

Apply the power rule and multiply exponents,

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

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

Step 1.4.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 1.4.4

Cancel the common factor of

$2$ .

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Step 1.4.4.1

Cancel the common factor.

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

Step 1.4.4.2

Rewrite the expression.

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

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

Step 1.4.5

Evaluate the exponent.

$v (4 + 4 \cdot 3)$

$v (4 + 4 \cdot 3)$

Step 1.5

Multiply

$4$ by

$3$ .

$v (4 + 12)$

$v (4 + 12)$

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

$v$ .

$16 v$

$16 v$

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