Trigonometry Examples

$v (\frac{1 - (- \frac{5}{\sqrt{41}})}{2})$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $\frac{5}{\sqrt{41}}$ by $\frac{\sqrt{41}}{\sqrt{41}}$ .

$v \frac{1 - - (\frac{5}{\sqrt{41}} \cdot \frac{\sqrt{41}}{\sqrt{41}})}{2}$

Step 1.2

Combine and simplify the denominator.

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Step 1.2.1

Multiply $\frac{5}{\sqrt{41}}$ by $\frac{\sqrt{41}}{\sqrt{41}}$ .

$v \frac{1 - - \frac{5 \sqrt{41}}{\sqrt{41} \sqrt{41}}}{2}$

Step 1.2.2

Raise $\sqrt{41}$ to the power of $1$ .

$v \frac{1 - - \frac{5 \sqrt{41}}{{\sqrt{41}}^{1} \sqrt{41}}}{2}$

Step 1.2.3

Raise $\sqrt{41}$ to the power of $1$ .

$v \frac{1 - - \frac{5 \sqrt{41}}{{\sqrt{41}}^{1} {\sqrt{41}}^{1}}}{2}$

Step 1.2.4

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

$v \frac{1 - - \frac{5 \sqrt{41}}{{\sqrt{41}}^{1 + 1}}}{2}$

Step 1.2.5

Add $1$ and $1$ .

$v \frac{1 - - \frac{5 \sqrt{41}}{{\sqrt{41}}^{2}}}{2}$

Step 1.2.6

Rewrite ${\sqrt{41}}^{2}$ as $41$ .

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Step 1.2.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{41}$ as $41^{\frac{1}{2}}$ .

$v \frac{1 - - \frac{5 \sqrt{41}}{{(41^{\frac{1}{2}})}^{2}}}{2}$

Step 1.2.6.2

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

$v \frac{1 - - \frac{5 \sqrt{41}}{41^{\frac{1}{2} \cdot 2}}}{2}$

Step 1.2.6.3

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

$v \frac{1 - - \frac{5 \sqrt{41}}{41^{\frac{2}{2}}}}{2}$

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.

$v \frac{1 - - \frac{5 \sqrt{41}}{41^{\frac{2}{2}}}}{2}$

Step 1.2.6.4.2

Rewrite the expression.

$v \frac{1 - - \frac{5 \sqrt{41}}{41^{1}}}{2}$

Step 1.2.6.5

Evaluate the exponent.

$v \frac{1 - - \frac{5 \sqrt{41}}{41}}{2}$

Step 1.3

Multiply $- - \frac{5 \sqrt{41}}{41}$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$v \frac{1 + 1 \frac{5 \sqrt{41}}{41}}{2}$

Step 1.3.2

Multiply $\frac{5 \sqrt{41}}{41}$ by $1$ .

$v \frac{1 + \frac{5 \sqrt{41}}{41}}{2}$

Step 1.4

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

$v \frac{\frac{41}{41} + \frac{5 \sqrt{41}}{41}}{2}$

Step 1.5

Combine the numerators over the common denominator.

$v \frac{\frac{41 + 5 \sqrt{41}}{41}}{2}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$v (\frac{41 + 5 \sqrt{41}}{41} \cdot \frac{1}{2})$

Step 3

Multiply $\frac{41 + 5 \sqrt{41}}{41} \cdot \frac{1}{2}$ .

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Step 3.1

Multiply $\frac{41 + 5 \sqrt{41}}{41}$ by $\frac{1}{2}$ .

$v \frac{41 + 5 \sqrt{41}}{41 \cdot 2}$

Step 3.2

Multiply $41$ by $2$ .

$v \frac{41 + 5 \sqrt{41}}{82}$

Step 4

Combine $v$ and $\frac{41 + 5 \sqrt{41}}{82}$ .

$\frac{v (41 + 5 \sqrt{41})}{82}$