Trigonometry Examples

$2 {(110)}^{2} (\frac{\sqrt{2}}{2}) (\frac{\sqrt{2}}{2})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Factor $2$ out of $2 {(110)}^{2} (\frac{\sqrt{2}}{2})$ .

$2 ({(110)}^{2} (\frac{\sqrt{2}}{2})) \cdot \frac{\sqrt{2}}{2}$

Step 1.2

Cancel the common factor.

$2 ({(110)}^{2} (\frac{\sqrt{2}}{2})) \cdot \frac{\sqrt{2}}{2}$

Step 1.3

Rewrite the expression.

${(110)}^{2} (\frac{\sqrt{2}}{2}) \cdot \sqrt{2}$

Step 2

Combine ${(110)}^{2}$ and $\frac{\sqrt{2}}{2}$ .

$\frac{{(110)}^{2} \sqrt{2}}{2} \cdot \sqrt{2}$

Step 3

Combine $\frac{{(110)}^{2} \sqrt{2}}{2}$ and $\sqrt{2}$ .

$\frac{{(110)}^{2} \sqrt{2} \sqrt{2}}{2}$

Step 4

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{(110)}^{2} ({\sqrt{2}}^{1} \sqrt{2})}{2}$

Step 5

Raise $\sqrt{2}$ to the power of $1$ .

$\frac{{(110)}^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})}{2}$

Step 6

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

$\frac{{(110)}^{2} {\sqrt{2}}^{1 + 1}}{2}$

Step 7

Add $1$ and $1$ .

$\frac{{(110)}^{2} {\sqrt{2}}^{2}}{2}$

Step 8

Simplify the numerator.

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Step 8.1

Raise $110$ to the power of $2$ .

$\frac{12100 {\sqrt{2}}^{2}}{2}$

Step 8.2

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

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Step 8.2.1

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

$\frac{12100 {(2^{\frac{1}{2}})}^{2}}{2}$

Step 8.2.2

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

$\frac{12100 \cdot 2^{\frac{1}{2} \cdot 2}}{2}$

Step 8.2.3

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

$\frac{12100 \cdot 2^{\frac{2}{2}}}{2}$

Step 8.2.4

Cancel the common factor of $2$ .

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Step 8.2.4.1

Cancel the common factor.

$\frac{12100 \cdot 2^{\frac{2}{2}}}{2}$

Step 8.2.4.2

Rewrite the expression.

$\frac{12100 \cdot 2^{1}}{2}$

Step 8.2.5

Evaluate the exponent.

$\frac{12100 \cdot 2}{2}$

Step 9

Simplify the expression.

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Step 9.1

Multiply $12100$ by $2$ .

$\frac{24200}{2}$

Step 9.2

Divide $24200$ by $2$ .

$12100$