Trigonometry Examples

$(- \frac{3}{5}) (\frac{7}{8}) - \frac{4}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1

Simplify each term.

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Step 1.1

Multiply $(- \frac{3}{5}) (\frac{7}{8})$ .

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Step 1.1.1

Multiply $\frac{7}{8}$ by $\frac{3}{5}$ .

$- \frac{7 \cdot 3}{8 \cdot 5} - \frac{4}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1.1.2

Multiply $7$ by $3$ .

$- \frac{21}{8 \cdot 5} - \frac{4}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1.1.3

Multiply $8$ by $5$ .

$- \frac{21}{40} - \frac{4}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1.2

Cancel the common factor of $4$ .

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Step 1.2.1

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$- \frac{21}{40} + \frac{- 4}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1.2.2

Factor $4$ out of $- 4$ .

$- \frac{21}{40} + \frac{4 (- 1)}{5} \cdot \frac{\sqrt{15}}{8}$

Step 1.2.3

Factor $4$ out of $8$ .

$- \frac{21}{40} + \frac{4 \cdot - 1}{5} \cdot \frac{\sqrt{15}}{4 \cdot 2}$

Step 1.2.4

Cancel the common factor.

$- \frac{21}{40} + \frac{4 \cdot - 1}{5} \cdot \frac{\sqrt{15}}{4 \cdot 2}$

Step 1.2.5

Rewrite the expression.

$- \frac{21}{40} + \frac{- 1}{5} \cdot \frac{\sqrt{15}}{2}$

Step 1.3

Multiply $\frac{- 1}{5}$ by $\frac{\sqrt{15}}{2}$ .

$- \frac{21}{40} + \frac{- \sqrt{15}}{5 \cdot 2}$

Step 1.4

Multiply $5$ by $2$ .

$- \frac{21}{40} + \frac{- \sqrt{15}}{10}$

Step 1.5

Move the negative in front of the fraction.

$- \frac{21}{40} - \frac{\sqrt{15}}{10}$

Step 2

To write $- \frac{\sqrt{15}}{10}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{21}{40} - \frac{\sqrt{15}}{10} \cdot \frac{4}{4}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{\sqrt{15}}{10}$ by $\frac{4}{4}$ .

$- \frac{21}{40} - \frac{\sqrt{15} \cdot 4}{10 \cdot 4}$

Step 3.2

Multiply $10$ by $4$ .

$- \frac{21}{40} - \frac{\sqrt{15} \cdot 4}{40}$

Step 4

Simplify the expression.

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Step 4.1

Combine the numerators over the common denominator.

$\frac{- 21 - \sqrt{15} \cdot 4}{40}$

Step 4.2

Multiply $4$ by $- 1$ .

$\frac{- 21 - 4 \sqrt{15}}{40}$

Step 5

Rewrite $- 21$ as $- 1 (21)$ .

$\frac{- 1 (21) - 4 \sqrt{15}}{40}$

Step 6

Factor $- 1$ out of $- 4 \sqrt{15}$ .

$\frac{- 1 (21) - (4 \sqrt{15})}{40}$

Step 7

Factor $- 1$ out of $- 1 (21) - (4 \sqrt{15})$ .

$\frac{- 1 (21 + 4 \sqrt{15})}{40}$

Step 8

Move the negative in front of the fraction.

$- \frac{21 + 4 \sqrt{15}}{40}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{21 + 4 \sqrt{15}}{40}$

Decimal Form:

$- 0.91229833 \dots$