Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Subtract $64$ from $289$ .

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

Step 6

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

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

Step 7

Simplify the numerator.

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Step 7.1

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

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

Step 7.2

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

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

Step 8

Simplify the denominator.

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Step 8.1

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

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

Step 8.2

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

$\frac{15}{17}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{15}{17}$

Decimal Form:

$0.88235294 \dots$