Trigonometry Examples

$\sqrt{1 - {(\frac{7}{8})}^{2}}$

Step 1

Apply the product rule to $\frac{7}{8}$ .

$\sqrt{1 - \frac{7^{2}}{8^{2}}}$

Step 2

Raise $7$ to the power of $2$ .

$\sqrt{1 - \frac{49}{8^{2}}}$

Step 3

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

$\sqrt{1 - \frac{49}{64}}$

Step 4

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

$\sqrt{\frac{64}{64} - \frac{49}{64}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{64 - 49}{64}}$

Step 6

Subtract $49$ from $64$ .

$\sqrt{\frac{15}{64}}$

Step 7

Rewrite $\sqrt{\frac{15}{64}}$ as $\frac{\sqrt{15}}{\sqrt{64}}$ .

$\frac{\sqrt{15}}{\sqrt{64}}$

Step 8

Simplify the denominator.

Tap for more steps...

Step 8.1

Rewrite $64$ as $8^{2}$ .

$\frac{\sqrt{15}}{\sqrt{8^{2}}}$

Step 8.2

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

$\frac{\sqrt{15}}{8}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{15}}{8}$

Decimal Form:

$0.48412291 \dots$