Trigonometry Examples

$\sqrt{\frac{1 - \frac{3}{4}}{1 + \frac{3}{4}}}$

Step 1

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

$\sqrt{\frac{\frac{4}{4} - \frac{3}{4}}{1 + \frac{3}{4}}}$

Step 2

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{4 - 3}{4}}{1 + \frac{3}{4}}}$

Step 3

Subtract $3$ from $4$ .

$\sqrt{\frac{\frac{1}{4}}{1 + \frac{3}{4}}}$

Step 4

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

$\sqrt{\frac{\frac{1}{4}}{\frac{4}{4} + \frac{3}{4}}}$

Step 5

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{1}{4}}{\frac{4 + 3}{4}}}$

Step 6

Add $4$ and $3$ .

$\sqrt{\frac{\frac{1}{4}}{\frac{7}{4}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{1}{4} \cdot \frac{4}{7}}$

Step 8

Cancel the common factor of $4$ .

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Step 8.1

Cancel the common factor.

$\sqrt{\frac{1}{4} \cdot \frac{4}{7}}$

Step 8.2

Rewrite the expression.

$\sqrt{\frac{1}{7}}$

Step 9

Rewrite $\sqrt{\frac{1}{7}}$ as $\frac{\sqrt{1}}{\sqrt{7}}$ .

$\frac{\sqrt{1}}{\sqrt{7}}$

Step 10

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{7}}$

Step 11

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

$\frac{1}{\sqrt{7}} \cdot \frac{\sqrt{7}}{\sqrt{7}}$

Step 12

Combine and simplify the denominator.

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Step 12.1

Multiply $\frac{1}{\sqrt{7}}$ by $\frac{\sqrt{7}}{\sqrt{7}}$ .

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

Step 12.2

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{7}}{{\sqrt{7}}^{1} \sqrt{7}}$

Step 12.3

Raise $\sqrt{7}$ to the power of $1$ .

$\frac{\sqrt{7}}{{\sqrt{7}}^{1} {\sqrt{7}}^{1}}$

Step 12.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\sqrt{7}}{{\sqrt{7}}^{1 + 1}}$

Step 12.5

Add $1$ and $1$ .

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

Step 12.6

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 12.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

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

Step 12.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{\sqrt{7}}{7^{\frac{1}{2} \cdot 2}}$

Step 12.6.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 12.6.4

Cancel the common factor of $2$ .

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Step 12.6.4.1

Cancel the common factor.

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

Step 12.6.4.2

Rewrite the expression.

$\frac{\sqrt{7}}{7^{1}}$

Step 12.6.5

Evaluate the exponent.

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

Step 13

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.37796447 \dots$