Trigonometry Examples

$(\frac{3}{5}) (\frac{4 \sqrt{41}}{41}) - \frac{4}{5} (- \frac{5 \sqrt{41}}{41})$

Step 1

Simplify each term.

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Step 1.1

Multiply $(\frac{3}{5}) (\frac{4 \sqrt{41}}{41})$ .

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Step 1.1.1

Multiply $\frac{3}{5}$ by $\frac{4 \sqrt{41}}{41}$ .

$\frac{3 (4 \sqrt{41})}{5 \cdot 41} - \frac{4}{5} \cdot (- \frac{5 \sqrt{41}}{41})$

Step 1.1.2

Multiply $4$ by $3$ .

$\frac{12 \sqrt{41}}{5 \cdot 41} - \frac{4}{5} \cdot (- \frac{5 \sqrt{41}}{41})$

Step 1.1.3

Multiply $5$ by $41$ .

$\frac{12 \sqrt{41}}{205} - \frac{4}{5} \cdot (- \frac{5 \sqrt{41}}{41})$

Step 1.2

Cancel the common factor of $5$ .

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Step 1.2.1

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

$\frac{12 \sqrt{41}}{205} + \frac{- 4}{5} \cdot (- \frac{5 \sqrt{41}}{41})$

Step 1.2.2

Move the leading negative in $- \frac{5 \sqrt{41}}{41}$ into the numerator.

$\frac{12 \sqrt{41}}{205} + \frac{- 4}{5} \cdot \frac{- 5 \sqrt{41}}{41}$

Step 1.2.3

Factor $5$ out of $- 5 \sqrt{41}$ .

$\frac{12 \sqrt{41}}{205} + \frac{- 4}{5} \cdot \frac{5 (- \sqrt{41})}{41}$

Step 1.2.4

Cancel the common factor.

$\frac{12 \sqrt{41}}{205} + \frac{- 4}{5} \cdot \frac{5 (- \sqrt{41})}{41}$

Step 1.2.5

Rewrite the expression.

$\frac{12 \sqrt{41}}{205} - 4 \cdot \frac{- \sqrt{41}}{41}$

Step 1.3

Combine $- 4$ and $\frac{- \sqrt{41}}{41}$ .

$\frac{12 \sqrt{41}}{205} + \frac{- 4 (- \sqrt{41})}{41}$

Step 1.4

Multiply $- 1$ by $- 4$ .

$\frac{12 \sqrt{41}}{205} + \frac{4 \sqrt{41}}{41}$

Step 2

To write $\frac{4 \sqrt{41}}{41}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{12 \sqrt{41}}{205} + \frac{4 \sqrt{41}}{41} \cdot \frac{5}{5}$

Step 3

Write each expression with a common denominator of $205$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4 \sqrt{41}}{41}$ by $\frac{5}{5}$ .

$\frac{12 \sqrt{41}}{205} + \frac{4 \sqrt{41} \cdot 5}{41 \cdot 5}$

Step 3.2

Multiply $41$ by $5$ .

$\frac{12 \sqrt{41}}{205} + \frac{4 \sqrt{41} \cdot 5}{205}$

Step 4

Combine the numerators over the common denominator.

$\frac{12 \sqrt{41} + 4 \sqrt{41} \cdot 5}{205}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $5$ by $4$ .

$\frac{12 \sqrt{41} + 20 \sqrt{41}}{205}$

Step 5.2

Add $12 \sqrt{41}$ and $20 \sqrt{41}$ .

$\frac{32 \sqrt{41}}{205}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{32 \sqrt{41}}{205}$

Decimal Form:

$0.99951207 \dots$