Trigonometry Examples

$\frac{4 y}{5 y} = \frac{A}{15 y^{2}}$

Step 1

Rewrite the equation as $\frac{A}{15 y^{2}} = \frac{4 y}{5 y}$ .

$\frac{A}{15 y^{2}} = \frac{4 y}{5 y}$

Step 2

Multiply both sides by $15 y^{2}$ .

$\frac{A}{15 y^{2}} (15 y^{2}) = \frac{4 y}{5 y} (15 y^{2})$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{A}{15 y^{2}} (15 y^{2})$ .

Tap for more steps...

Step 3.1.1.1

Rewrite using the commutative property of multiplication.

$15 \frac{A}{15 y^{2}} y^{2} = \frac{4 y}{5 y} (15 y^{2})$

Step 3.1.1.2

Cancel the common factor of $15$ .

Tap for more steps...

Step 3.1.1.2.1

Factor $15$ out of $15 y^{2}$ .

$15 \frac{A}{15 (y^{2})} y^{2} = \frac{4 y}{5 y} (15 y^{2})$

Step 3.1.1.2.2

Cancel the common factor.

$15 \frac{A}{15 y^{2}} y^{2} = \frac{4 y}{5 y} (15 y^{2})$

Step 3.1.1.2.3

Rewrite the expression.

$\frac{A}{y^{2}} y^{2} = \frac{4 y}{5 y} (15 y^{2})$

Step 3.1.1.3

Cancel the common factor of $y^{2}$ .

Tap for more steps...

Step 3.1.1.3.1

Cancel the common factor.

$\frac{A}{y^{2}} y^{2} = \frac{4 y}{5 y} (15 y^{2})$

Step 3.1.1.3.2

Rewrite the expression.

$A = \frac{4 y}{5 y} (15 y^{2})$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\frac{4 y}{5 y} (15 y^{2})$ .

Tap for more steps...

Step 3.2.1.1

Rewrite using the commutative property of multiplication.

$A = 15 \frac{4 y}{5 y} y^{2}$

Step 3.2.1.2

Cancel the common factor of $5$ .

Tap for more steps...

Step 3.2.1.2.1

Factor $5$ out of $15$ .

$A = 5 (3) \frac{4 y}{5 y} y^{2}$

Step 3.2.1.2.2

Factor $5$ out of $5 y$ .

$A = 5 (3) \frac{4 y}{5 (y)} y^{2}$

Step 3.2.1.2.3

Cancel the common factor.

$A = 5 \cdot 3 \frac{4 y}{5 y} y^{2}$

Step 3.2.1.2.4

Rewrite the expression.

$A = 3 \frac{4 y}{y} y^{2}$

Step 3.2.1.3

Combine $3$ and $\frac{4 y}{y}$ .

$A = \frac{3 (4 y)}{y} y^{2}$

Step 3.2.1.4

Multiply $4$ by $3$ .

$A = \frac{12 y}{y} y^{2}$

Step 3.2.1.5

Cancel the common factor of $y$ .

Tap for more steps...

Step 3.2.1.5.1

Factor $y$ out of $y^{2}$ .

$A = \frac{12 y}{y} (y \cdot y)$

Step 3.2.1.5.2

Cancel the common factor.

$A = \frac{12 y}{y} (y \cdot y)$

Step 3.2.1.5.3

Rewrite the expression.

$A = 12 y \cdot y$

Step 3.2.1.6

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

$A = 12 (y^{1} y)$

Step 3.2.1.7

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

$A = 12 (y^{1} y^{1})$

Step 3.2.1.8

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

$A = 12 y^{1 + 1}$

Step 3.2.1.9

Add $1$ and $1$ .

$A = 12 y^{2}$