Trigonometry Examples

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

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1

Apply the product rule to $- \frac{8}{17}$ .

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

Step 1.2

Apply the product rule to $\frac{8}{17}$ .

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

Step 2

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 2.1

Move ${(- 1)}^{2}$ .

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

Step 2.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 2.2.1

Raise $- 1$ to the power of $1$ .

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

$\sqrt{1 + {(- 1)}^{3} \frac{8^{2}}{17^{2}}}$

Step 3

Raise $- 1$ to the power of $3$ .

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

Step 4

Raise $8$ to the power of $2$ .

$\sqrt{1 - \frac{64}{17^{2}}}$

Step 5

Raise $17$ to the power of $2$ .

$\sqrt{1 - \frac{64}{289}}$

Step 6

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

$\sqrt{\frac{289}{289} - \frac{64}{289}}$

Step 7

Combine the numerators over the common denominator.

$\sqrt{\frac{289 - 64}{289}}$

Step 8

Subtract $64$ from $289$ .

$\sqrt{\frac{225}{289}}$

Step 9

Rewrite $\sqrt{\frac{225}{289}}$ as $\frac{\sqrt{225}}{\sqrt{289}}$ .

$\frac{\sqrt{225}}{\sqrt{289}}$

Step 10

Simplify the numerator.

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Step 10.1

Rewrite $225$ as $15^{2}$ .

$\frac{\sqrt{15^{2}}}{\sqrt{289}}$

Step 10.2

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

$\frac{15}{\sqrt{289}}$

Step 11

Simplify the denominator.

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Step 11.1

Rewrite $289$ as $17^{2}$ .

$\frac{15}{\sqrt{17^{2}}}$

Step 11.2

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

$\frac{15}{17}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{17}$

Decimal Form:

$0.88235294 \dots$