Trigonometry Examples

$- v \frac{1 + \frac{\sqrt{- 5}}{3}}{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $- 5$ as $- 1 (5)$ .

$- v \frac{1 + \frac{\sqrt{- 1 (5)}}{3}}{2}$

Step 1.2

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$- v \frac{1 + \frac{\sqrt{- 1} \cdot \sqrt{5}}{3}}{2}$

Step 1.3

Rewrite $\sqrt{- 1}$ as $i$ .

$- v \frac{1 + \frac{i \sqrt{5}}{3}}{2}$

Step 2

Simplify the numerator.

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Step 2.1

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

$- v \frac{\frac{3}{3} + \frac{i \sqrt{5}}{3}}{2}$

Step 2.2

Combine the numerators over the common denominator.

$- v \frac{\frac{3 + i \sqrt{5}}{3}}{2}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- v (\frac{3 + i \sqrt{5}}{3} \cdot \frac{1}{2})$

Step 4

Multiply $\frac{3 + i \sqrt{5}}{3} \cdot \frac{1}{2}$ .

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Step 4.1

Multiply $\frac{3 + i \sqrt{5}}{3}$ by $\frac{1}{2}$ .

$- v \frac{3 + i \sqrt{5}}{3 \cdot 2}$

Step 4.2

Multiply $3$ by $2$ .

$- v \frac{3 + i \sqrt{5}}{6}$

Step 5

Combine $\frac{3 + i \sqrt{5}}{6}$ and $v$ .

$- \frac{(3 + i \sqrt{5}) v}{6}$