Trigonometry Examples

$\sqrt{1 + {(\frac{8}{9})}^{2}}$

Step 1

Apply the product rule to $\frac{8}{9}$ .

$\sqrt{1 + \frac{8^{2}}{9^{2}}}$

Step 2

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

$\sqrt{1 + \frac{64}{9^{2}}}$

Step 3

Raise $9$ to the power of $2$ .

$\sqrt{1 + \frac{64}{81}}$

Step 4

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

$\sqrt{\frac{81}{81} + \frac{64}{81}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{81 + 64}{81}}$

Step 6

Add $81$ and $64$ .

$\sqrt{\frac{145}{81}}$

Step 7

Rewrite $\sqrt{\frac{145}{81}}$ as $\frac{\sqrt{145}}{\sqrt{81}}$ .

$\frac{\sqrt{145}}{\sqrt{81}}$

Step 8

Simplify the denominator.

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Step 8.1

Rewrite $81$ as $9^{2}$ .

$\frac{\sqrt{145}}{\sqrt{9^{2}}}$

Step 8.2

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

$\frac{\sqrt{145}}{9}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{145}}{9}$

Decimal Form:

$1.33795495 \dots$