Trigonometry Examples

$\sqrt{1 - {(\frac{9}{25})}^{2}}$

Step 1

Apply the product rule to $\frac{9}{25}$ .

$\sqrt{1 - \frac{9^{2}}{25^{2}}}$

Step 2

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

$\sqrt{1 - \frac{81}{25^{2}}}$

Step 3

Raise $25$ to the power of $2$ .

$\sqrt{1 - \frac{81}{625}}$

Step 4

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

$\sqrt{\frac{625}{625} - \frac{81}{625}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{625 - 81}{625}}$

Step 6

Subtract $81$ from $625$ .

$\sqrt{\frac{544}{625}}$

Step 7

Rewrite $\sqrt{\frac{544}{625}}$ as $\frac{\sqrt{544}}{\sqrt{625}}$ .

$\frac{\sqrt{544}}{\sqrt{625}}$

Step 8

Simplify the numerator.

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Step 8.1

Rewrite $544$ as $4^{2} \cdot 34$ .

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Step 8.1.1

Factor $16$ out of $544$ .

$\frac{\sqrt{16 (34)}}{\sqrt{625}}$

Step 8.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2} \cdot 34}}{\sqrt{625}}$

Step 8.2

Pull terms out from under the radical.

$\frac{4 \sqrt{34}}{\sqrt{625}}$

Step 9

Simplify the denominator.

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Step 9.1

Rewrite $625$ as $25^{2}$ .

$\frac{4 \sqrt{34}}{\sqrt{25^{2}}}$

Step 9.2

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

$\frac{4 \sqrt{34}}{25}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{4 \sqrt{34}}{25}$

Decimal Form:

$0.93295230 \dots$