Trigonometry Examples

$2 (\frac{7}{19}) (\frac{- \sqrt{312}}{19})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $312$ as $2^{2} \cdot 78$ .

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Step 1.1.1

Factor $4$ out of $312$ .

$2 (\frac{7}{19}) \cdot \frac{- \sqrt{4 (78)}}{19}$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$2 (\frac{7}{19}) \cdot \frac{- \sqrt{2^{2} \cdot 78}}{19}$

Step 1.2

Pull terms out from under the radical.

$2 (\frac{7}{19}) \cdot \frac{- 1 \cdot 2 \sqrt{78}}{19}$

Step 1.3

Multiply $- 1$ by $2$ .

$2 (\frac{7}{19}) \cdot \frac{- 2 \sqrt{78}}{19}$

Step 2

Multiply $2 (\frac{7}{19})$ .

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Step 2.1

Combine $2$ and $\frac{7}{19}$ .

$\frac{2 \cdot 7}{19} \cdot \frac{- 2 \sqrt{78}}{19}$

Step 2.2

Multiply $2$ by $7$ .

$\frac{14}{19} \cdot \frac{- 2 \sqrt{78}}{19}$

Step 3

Move the negative in front of the fraction.

$\frac{14}{19} \cdot (- \frac{2 \sqrt{78}}{19})$

Step 4

Multiply $\frac{14}{19} (- \frac{2 \sqrt{78}}{19})$ .

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Step 4.1

Multiply $\frac{14}{19}$ by $\frac{2 \sqrt{78}}{19}$ .

$- \frac{14 (2 \sqrt{78})}{19 \cdot 19}$

Step 4.2

Multiply $2$ by $14$ .

$- \frac{28 \sqrt{78}}{19 \cdot 19}$

Step 4.3

Multiply $19$ by $19$ .

$- \frac{28 \sqrt{78}}{361}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{28 \sqrt{78}}{361}$

Decimal Form:

$- 0.68501192 \dots$