Trigonometry Examples

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

Step 1

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

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Step 1.1

Multiply $- 1$ by $- 1$ .

$- \sqrt{\frac{1 + 1 (\frac{8}{17})}{2}}$

Step 1.2

Multiply $\frac{8}{17}$ by $1$ .

$- \sqrt{\frac{1 + \frac{8}{17}}{2}}$

Step 2

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

$- \sqrt{\frac{\frac{17}{17} + \frac{8}{17}}{2}}$

Step 3

Combine the numerators over the common denominator.

$- \sqrt{\frac{\frac{17 + 8}{17}}{2}}$

Step 4

Add $17$ and $8$ .

$- \sqrt{\frac{\frac{25}{17}}{2}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$- \sqrt{\frac{25}{17} \cdot \frac{1}{2}}$

Step 6

Multiply $\frac{25}{17} \cdot \frac{1}{2}$ .

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Step 6.1

Multiply $\frac{25}{17}$ by $\frac{1}{2}$ .

$- \sqrt{\frac{25}{17 \cdot 2}}$

Step 6.2

Multiply $17$ by $2$ .

$- \sqrt{\frac{25}{34}}$

Step 7

Rewrite $\sqrt{\frac{25}{34}}$ as $\frac{\sqrt{25}}{\sqrt{34}}$ .

$- \frac{\sqrt{25}}{\sqrt{34}}$

Step 8

Simplify the numerator.

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Step 8.1

Rewrite $25$ as $5^{2}$ .

$- \frac{\sqrt{5^{2}}}{\sqrt{34}}$

Step 8.2

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{5}{\sqrt{34}}$

Step 9

Multiply $\frac{5}{\sqrt{34}}$ by $\frac{\sqrt{34}}{\sqrt{34}}$ .

$- (\frac{5}{\sqrt{34}} \cdot \frac{\sqrt{34}}{\sqrt{34}})$

Step 10

Combine and simplify the denominator.

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Step 10.1

Multiply $\frac{5}{\sqrt{34}}$ by $\frac{\sqrt{34}}{\sqrt{34}}$ .

$- \frac{5 \sqrt{34}}{\sqrt{34} \sqrt{34}}$

Step 10.2

Raise $\sqrt{34}$ to the power of $1$ .

$- \frac{5 \sqrt{34}}{{\sqrt{34}}^{1} \sqrt{34}}$

Step 10.3

Raise $\sqrt{34}$ to the power of $1$ .

$- \frac{5 \sqrt{34}}{{\sqrt{34}}^{1} {\sqrt{34}}^{1}}$

Step 10.4

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

$- \frac{5 \sqrt{34}}{{\sqrt{34}}^{1 + 1}}$

Step 10.5

Add $1$ and $1$ .

$- \frac{5 \sqrt{34}}{{\sqrt{34}}^{2}}$

Step 10.6

Rewrite ${\sqrt{34}}^{2}$ as $34$ .

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Step 10.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{34}$ as $34^{\frac{1}{2}}$ .

$- \frac{5 \sqrt{34}}{{(34^{\frac{1}{2}})}^{2}}$

Step 10.6.2

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

$- \frac{5 \sqrt{34}}{34^{\frac{1}{2} \cdot 2}}$

Step 10.6.3

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

$- \frac{5 \sqrt{34}}{34^{\frac{2}{2}}}$

Step 10.6.4

Cancel the common factor of $2$ .

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Step 10.6.4.1

Cancel the common factor.

$- \frac{5 \sqrt{34}}{34^{\frac{2}{2}}}$

Step 10.6.4.2

Rewrite the expression.

$- \frac{5 \sqrt{34}}{34^{1}}$

Step 10.6.5

Evaluate the exponent.

$- \frac{5 \sqrt{34}}{34}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$- \frac{5 \sqrt{34}}{34}$

Decimal Form:

$- 0.85749292 \dots$