Algebra Examples

$y = 3 \sin (\frac{3}{4}) (\frac{8 π}{9} + \frac{2 π}{3}) - 5$

Step 1

Simplify each term.

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Step 1.1

Evaluate $\sin (\frac{3}{4})$ .

$y = 3 \cdot 0.68163876 (\frac{8 π}{9} + \frac{2 π}{3}) - 5$

Step 1.2

Multiply $3$ by $0.68163876$ .

$y = 2.04491628 (\frac{8 π}{9} + \frac{2 π}{3}) - 5$

Step 1.3

To write $\frac{2 π}{3}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 2.04491628 (\frac{8 π}{9} + \frac{2 π}{3} \cdot \frac{3}{3}) - 5$

Step 1.4

Write each expression with a common denominator of $9$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{2 π}{3}$ by $\frac{3}{3}$ .

$y = 2.04491628 (\frac{8 π}{9} + \frac{2 π \cdot 3}{3 \cdot 3}) - 5$

Step 1.4.2

Multiply $3$ by $3$ .

$y = 2.04491628 (\frac{8 π}{9} + \frac{2 π \cdot 3}{9}) - 5$

Step 1.5

Combine the numerators over the common denominator.

$y = 2.04491628 \frac{8 π + 2 π \cdot 3}{9} - 5$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Multiply $3$ by $2$ .

$y = 2.04491628 \frac{8 π + 6 π}{9} - 5$

Step 1.6.2

Add $8 π$ and $6 π$ .

$y = 2.04491628 \frac{14 π}{9} - 5$

Step 1.7

Multiply $2.04491628 \frac{14 π}{9}$ .

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Step 1.7.1

Combine $2.04491628$ and $\frac{14 π}{9}$ .

$y = \frac{2.04491628 (14 π)}{9} - 5$

Step 1.7.2

Multiply $14$ by $2.04491628$ .

$y = \frac{28.62882792 π}{9} - 5$

Step 1.7.3

Multiply $28.62882792$ by $π$ .

$y = \frac{89.94011547}{9} - 5$

Step 1.8

Divide $89.94011547$ by $9$ .

$y = 9.99334616 - 5$

Step 2

Subtract $5$ from $9.99334616$ .

$y = 4.99334616$