Trigonometry Examples

$v (\frac{1 - \frac{1}{\sqrt{82}}}{2})$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $\frac{1}{\sqrt{82}}$ by $\frac{\sqrt{82}}{\sqrt{82}}$ .

$v \frac{1 - (\frac{1}{\sqrt{82}} \cdot \frac{\sqrt{82}}{\sqrt{82}})}{2}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{1}{\sqrt{82}}$ by $\frac{\sqrt{82}}{\sqrt{82}}$ .

$v \frac{1 - \frac{\sqrt{82}}{\sqrt{82} \sqrt{82}}}{2}$

Step 1.2.2

Raise $\sqrt{82}$ to the power of $1$ .

$v \frac{1 - \frac{\sqrt{82}}{{\sqrt{82}}^{1} \sqrt{82}}}{2}$

Step 1.2.3

Raise $\sqrt{82}$ to the power of $1$ .

$v \frac{1 - \frac{\sqrt{82}}{{\sqrt{82}}^{1} {\sqrt{82}}^{1}}}{2}$

Step 1.2.4

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

$v \frac{1 - \frac{\sqrt{82}}{{\sqrt{82}}^{1 + 1}}}{2}$

Step 1.2.5

Add $1$ and $1$ .

$v \frac{1 - \frac{\sqrt{82}}{{\sqrt{82}}^{2}}}{2}$

Step 1.2.6

Rewrite ${\sqrt{82}}^{2}$ as $82$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{82}$ as $82^{\frac{1}{2}}$ .

$v \frac{1 - \frac{\sqrt{82}}{{(82^{\frac{1}{2}})}^{2}}}{2}$

Step 1.2.6.2

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

$v \frac{1 - \frac{\sqrt{82}}{82^{\frac{1}{2} \cdot 2}}}{2}$

Step 1.2.6.3

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

$v \frac{1 - \frac{\sqrt{82}}{82^{\frac{2}{2}}}}{2}$

Step 1.2.6.4

Cancel the common factor of $2$ .

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Step 1.2.6.4.1

Cancel the common factor.

$v \frac{1 - \frac{\sqrt{82}}{82^{\frac{2}{2}}}}{2}$

Step 1.2.6.4.2

Rewrite the expression.

$v \frac{1 - \frac{\sqrt{82}}{82^{1}}}{2}$

Step 1.2.6.5

Evaluate the exponent.

$v \frac{1 - \frac{\sqrt{82}}{82}}{2}$

Step 1.3

Write $1$ as a fraction with a common denominator.

$v \frac{\frac{82}{82} - \frac{\sqrt{82}}{82}}{2}$

Step 1.4

Combine the numerators over the common denominator.

$v \frac{\frac{82 - \sqrt{82}}{82}}{2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$v (\frac{82 - \sqrt{82}}{82} \cdot \frac{1}{2})$

Step 3

Multiply $\frac{82 - \sqrt{82}}{82} \cdot \frac{1}{2}$ .

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Step 3.1

Multiply $\frac{82 - \sqrt{82}}{82}$ by $\frac{1}{2}$ .

$v \frac{82 - \sqrt{82}}{82 \cdot 2}$

Step 3.2

Multiply $82$ by $2$ .

$v \frac{82 - \sqrt{82}}{164}$

Step 4

Combine $v$ and $\frac{82 - \sqrt{82}}{164}$ .

$\frac{v (82 - \sqrt{82})}{164}$