Trigonometry Examples

$\sqrt{1 - {(\frac{24}{25})}^{2}}$

Step 1

Apply the product rule to $\frac{24}{25}$ .

$\sqrt{1 - \frac{24^{2}}{25^{2}}}$

Step 2

Raise $24$ to the power of $2$ .

$\sqrt{1 - \frac{576}{25^{2}}}$

Step 3

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

$\sqrt{1 - \frac{576}{625}}$

Step 4

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

$\sqrt{\frac{625}{625} - \frac{576}{625}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{625 - 576}{625}}$

Step 6

Subtract $576$ from $625$ .

$\sqrt{\frac{49}{625}}$

Step 7

Rewrite $\sqrt{\frac{49}{625}}$ as $\frac{\sqrt{49}}{\sqrt{625}}$ .

$\frac{\sqrt{49}}{\sqrt{625}}$

Step 8

Simplify the numerator.

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Step 8.1

Rewrite $49$ as $7^{2}$ .

$\frac{\sqrt{7^{2}}}{\sqrt{625}}$

Step 8.2

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

$\frac{7}{\sqrt{625}}$

Step 9

Simplify the denominator.

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Step 9.1

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

$\frac{7}{\sqrt{25^{2}}}$

Step 9.2

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

$\frac{7}{25}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{7}{25}$

Decimal Form:

$0.28$