Trigonometry Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $2$ .

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

Step 1.2

Combine $- 2$ and $\frac{7}{24}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1.1

Apply the product rule to $- \frac{7}{24}$ .

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

Step 2.1.2

Apply the product rule to $\frac{7}{24}$ .

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

Step 2.2

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

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Step 2.2.1

Move ${(- 1)}^{2}$ .

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

Step 2.2.2

Multiply ${(- 1)}^{2}$ by $- 1$ .

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Step 2.2.2.1

Raise $- 1$ to the power of $1$ .

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

Step 2.2.2.2

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

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

Step 2.2.3

Add $2$ and $1$ .

$\frac{\frac{- 2 \cdot 7}{24}}{1 + {(- 1)}^{3} \frac{7^{2}}{24^{2}}}$

Step 2.3

Raise $- 1$ to the power of $3$ .

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

Step 2.4

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

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

Step 2.5

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

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

Step 2.6

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

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

Step 2.7

Combine the numerators over the common denominator.

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

Step 2.8

Subtract $49$ from $576$ .

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

Step 3

Multiply $- 2$ by $7$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 14$ and $24$ .

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Step 4.1.1

Factor $2$ out of $- 14$ .

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

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $24$ .

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

Move the negative in front of the fraction.

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

Step 5

Multiply the numerator by the reciprocal of the denominator.

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

Step 6

Cancel the common factor of $12$ .

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Step 6.1

Move the leading negative in $- \frac{7}{12}$ into the numerator.

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

Step 6.2

Factor $12$ out of $576$ .

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

Step 6.3

Cancel the common factor.

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

Step 6.4

Rewrite the expression.

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

Step 7

Combine $- 7$ and $\frac{48}{527}$ .

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

Step 8

Simplify the expression.

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Step 8.1

Multiply $- 7$ by $48$ .

$\frac{- 336}{527}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{336}{527}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{336}{527}$

Decimal Form:

$- 0.63757115 \dots$