Trigonometry Examples

$\frac{2 (- \frac{15}{8})}{1 - {(- \frac{15}{8})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Multiply $- 1$ by $2$ .

$\frac{- 2 (\frac{15}{8})}{1 - {(- \frac{15}{8})}^{2}}$

Step 1.2

Combine $- 2$ and $\frac{15}{8}$ .

$\frac{\frac{- 2 \cdot 15}{8}}{1 - {(- \frac{15}{8})}^{2}}$

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 $- \frac{15}{8}$ .

$\frac{\frac{- 2 \cdot 15}{8}}{1 - ({(- 1)}^{2} {(\frac{15}{8})}^{2})}$

Step 2.1.2

Apply the product rule to $\frac{15}{8}$ .

$\frac{\frac{- 2 \cdot 15}{8}}{1 - ({(- 1)}^{2} \frac{15^{2}}{8^{2}})}$

Step 2.2

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

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Step 2.2.1

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

$\frac{\frac{- 2 \cdot 15}{8}}{1 + {(- 1)}^{2} \cdot - 1 \frac{15^{2}}{8^{2}}}$

Step 2.2.2

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

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Step 2.2.2.1

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

$\frac{\frac{- 2 \cdot 15}{8}}{1 + {(- 1)}^{2} \cdot {(- 1)}^{1} \frac{15^{2}}{8^{2}}}$

Step 2.2.2.2

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

$\frac{\frac{- 2 \cdot 15}{8}}{1 + {(- 1)}^{2 + 1} \frac{15^{2}}{8^{2}}}$

Step 2.2.3

Add $2$ and $1$ .

$\frac{\frac{- 2 \cdot 15}{8}}{1 + {(- 1)}^{3} \frac{15^{2}}{8^{2}}}$

Step 2.3

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

$\frac{\frac{- 2 \cdot 15}{8}}{1 - \frac{15^{2}}{8^{2}}}$

Step 2.4

Raise $15$ to the power of $2$ .

$\frac{\frac{- 2 \cdot 15}{8}}{1 - \frac{225}{8^{2}}}$

Step 2.5

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

$\frac{\frac{- 2 \cdot 15}{8}}{1 - \frac{225}{64}}$

Step 2.6

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

$\frac{\frac{- 2 \cdot 15}{8}}{\frac{64}{64} - \frac{225}{64}}$

Step 2.7

Combine the numerators over the common denominator.

$\frac{\frac{- 2 \cdot 15}{8}}{\frac{64 - 225}{64}}$

Step 2.8

Subtract $225$ from $64$ .

$\frac{\frac{- 2 \cdot 15}{8}}{\frac{- 161}{64}}$

Step 2.9

Move the negative in front of the fraction.

$\frac{\frac{- 2 \cdot 15}{8}}{- \frac{161}{64}}$

Step 3

Multiply $- 2$ by $15$ .

$\frac{\frac{- 30}{8}}{- \frac{161}{64}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $- 30$ and $8$ .

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Step 4.1.1

Factor $2$ out of $- 30$ .

$\frac{\frac{2 (- 15)}{8}}{- \frac{161}{64}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $8$ .

$\frac{\frac{2 \cdot - 15}{2 \cdot 4}}{- \frac{161}{64}}$

Step 4.1.2.2

Cancel the common factor.

$\frac{\frac{2 \cdot - 15}{2 \cdot 4}}{- \frac{161}{64}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{\frac{- 15}{4}}{- \frac{161}{64}}$

Step 4.2

Move the negative in front of the fraction.

$\frac{- \frac{15}{4}}{- \frac{161}{64}}$

Step 5

Dividing two negative values results in a positive value.

$\frac{\frac{15}{4}}{\frac{161}{64}}$

Step 6

Multiply the numerator by the reciprocal of the denominator.

$\frac{15}{4} \cdot \frac{64}{161}$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Factor $4$ out of $64$ .

$\frac{15}{4} \cdot \frac{4 (16)}{161}$

Step 7.2

Cancel the common factor.

$\frac{15}{4} \cdot \frac{4 \cdot 16}{161}$

Step 7.3

Rewrite the expression.

$15 (\frac{16}{161})$

Step 8

Combine $15$ and $\frac{16}{161}$ .

$\frac{15 \cdot 16}{161}$

Step 9

Multiply $15$ by $16$ .

$\frac{240}{161}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{240}{161}$

Decimal Form:

$1.49068322 \dots$

Mixed Number Form:

$1 \frac{79}{161}$