Trigonometry Examples

\frac{2 (\frac{7}{24})}{1 - {(\frac{7}{24})}^{2}}

$\frac{2 (\frac{7}{24})}{1 - {(\frac{7}{24})}^{2}}$

Step 1

Combine

2

$2$ and

\frac{7}{24}

$\frac{7}{24}$ .

\frac{\frac{2 \cdot 7}{24}}{1 - {(\frac{7}{24})}^{2}}

$\frac{\frac{2 \cdot 7}{24}}{1 - {(\frac{7}{24})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to

\frac{7}{24}

$\frac{7}{24}$ .

\frac{\frac{2 \cdot 7}{24}}{1 - \frac{7^{2}}{24^{2}}}

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{7^{2}}{24^{2}}}$

Step 2.2

Raise

7

$7$ to the power of

2

$2$ .

\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{24^{2}}}

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{24^{2}}}$

Step 2.3

Raise

24

$24$ to the power of

2

$2$ .

\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{576}}

$\frac{\frac{2 \cdot 7}{24}}{1 - \frac{49}{576}}$

Step 2.4

Write

1

$1$ as a fraction with a common denominator.

\frac{\frac{2 \cdot 7}{24}}{\frac{576}{576} - \frac{49}{576}}

$\frac{\frac{2 \cdot 7}{24}}{\frac{576}{576} - \frac{49}{576}}$

Step 2.5

Combine the numerators over the common denominator.

\frac{\frac{2 \cdot 7}{24}}{\frac{576 - 49}{576}}

$\frac{\frac{2 \cdot 7}{24}}{\frac{576 - 49}{576}}$

Step 2.6

Subtract

49

$49$ from

576

$576$ .

\frac{\frac{2 \cdot 7}{24}}{\frac{527}{576}}

$\frac{\frac{2 \cdot 7}{24}}{\frac{527}{576}}$

\frac{\frac{2 \cdot 7}{24}}{\frac{527}{576}}

$\frac{\frac{2 \cdot 7}{24}}{\frac{527}{576}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply

2

$2$ by

7

$7$ .

\frac{\frac{14}{24}}{\frac{527}{576}}

$\frac{\frac{14}{24}}{\frac{527}{576}}$

Step 3.2

Cancel the common factor of

14

$14$ and

24

$24$ .

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Step 3.2.1

Factor

2

$2$ out of

14

$14$ .

\frac{\frac{2 (7)}{24}}{\frac{527}{576}}

$\frac{\frac{2 (7)}{24}}{\frac{527}{576}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor

2

$2$ out of

24

$24$ .

\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}

$\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}$

Step 3.2.2.2

Cancel the common factor.

\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}

$\frac{\frac{2 \cdot 7}{2 \cdot 12}}{\frac{527}{576}}$

Step 3.2.2.3

Rewrite the expression.

\frac{\frac{7}{12}}{\frac{527}{576}}

$\frac{\frac{7}{12}}{\frac{527}{576}}$

\frac{\frac{7}{12}}{\frac{527}{576}}

$\frac{\frac{7}{12}}{\frac{527}{576}}$

\frac{\frac{7}{12}}{\frac{527}{576}}

$\frac{\frac{7}{12}}{\frac{527}{576}}$

\frac{\frac{7}{12}}{\frac{527}{576}}

$\frac{\frac{7}{12}}{\frac{527}{576}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

\frac{7}{12} \cdot \frac{576}{527}

$\frac{7}{12} \cdot \frac{576}{527}$

Step 5

Cancel the common factor of

12

$12$ .

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Step 5.1

Factor

12

$12$ out of

576

$576$ .

\frac{7}{12} \cdot \frac{12 (48)}{527}

$\frac{7}{12} \cdot \frac{12 (48)}{527}$

Step 5.2

Cancel the common factor.

\frac{7}{12} \cdot \frac{12 \cdot 48}{527}

$\frac{7}{12} \cdot \frac{12 \cdot 48}{527}$

Step 5.3

Rewrite the expression.

7 (\frac{48}{527})

$7 (\frac{48}{527})$

7 (\frac{48}{527})

$7 (\frac{48}{527})$

Step 6

Combine

7

$7$ and

\frac{48}{527}

$\frac{48}{527}$ .

\frac{7 \cdot 48}{527}

$\frac{7 \cdot 48}{527}$

Step 7

Multiply

7

$7$ by

48

$48$ .

\frac{336}{527}

$\frac{336}{527}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{336}{527}

$\frac{336}{527}$

Decimal Form:

0.63757115 \dots

$0.63757115 \dots$