Trigonometry Examples

$2 (\frac{4 \sqrt{17}}{17}) (- \frac{\sqrt{17}}{17})$

Step 1

Multiply $2 (\frac{4 \sqrt{17}}{17})$ .

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Step 1.1

Combine $2$ and $\frac{4 \sqrt{17}}{17}$ .

$\frac{2 (4 \sqrt{17})}{17} \cdot (- \frac{\sqrt{17}}{17})$

Step 1.2

Multiply $4$ by $2$ .

$\frac{8 \sqrt{17}}{17} \cdot (- \frac{\sqrt{17}}{17})$

Step 2

Multiply $\frac{8 \sqrt{17}}{17} (- \frac{\sqrt{17}}{17})$ .

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Step 2.1

Multiply $\frac{8 \sqrt{17}}{17}$ by $\frac{\sqrt{17}}{17}$ .

$- \frac{8 \sqrt{17} \sqrt{17}}{17 \cdot 17}$

Step 2.2

Raise $\sqrt{17}$ to the power of $1$ .

$- \frac{8 ({\sqrt{17}}^{1} \sqrt{17})}{17 \cdot 17}$

Step 2.3

Raise $\sqrt{17}$ to the power of $1$ .

$- \frac{8 ({\sqrt{17}}^{1} {\sqrt{17}}^{1})}{17 \cdot 17}$

Step 2.4

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

$- \frac{8 {\sqrt{17}}^{1 + 1}}{17 \cdot 17}$

Step 2.5

Add $1$ and $1$ .

$- \frac{8 {\sqrt{17}}^{2}}{17 \cdot 17}$

Step 2.6

Multiply $17$ by $17$ .

$- \frac{8 {\sqrt{17}}^{2}}{289}$

Step 3

Rewrite ${\sqrt{17}}^{2}$ as $17$ .

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{17}$ as $17^{\frac{1}{2}}$ .

$- \frac{8 {(17^{\frac{1}{2}})}^{2}}{289}$

Step 3.2

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

$- \frac{8 \cdot 17^{\frac{1}{2} \cdot 2}}{289}$

Step 3.3

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

$- \frac{8 \cdot 17^{\frac{2}{2}}}{289}$

Step 3.4

Cancel the common factor of $2$ .

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Step 3.4.1

Cancel the common factor.

$- \frac{8 \cdot 17^{\frac{2}{2}}}{289}$

Step 3.4.2

Rewrite the expression.

$- \frac{8 \cdot 17^{1}}{289}$

Step 3.5

Evaluate the exponent.

$- \frac{8 \cdot 17}{289}$

Step 4

Multiply $8$ by $17$ .

$- \frac{136}{289}$

Step 5

Cancel the common factor of $136$ and $289$ .

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Step 5.1

Factor $17$ out of $136$ .

$- \frac{17 (8)}{289}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $17$ out of $289$ .

$- \frac{17 \cdot 8}{17 \cdot 17}$

Step 5.2.2

Cancel the common factor.

$- \frac{17 \cdot 8}{17 \cdot 17}$

Step 5.2.3

Rewrite the expression.

$- \frac{8}{17}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{8}{17}$

Decimal Form:

$- 0.47058823 \dots$