Algebra Examples

$r = \frac{3}{\sin (θ)}$

Step 1

Since $\sin (θ) = \frac{y}{r}$ , replace $\sin (θ)$ with $\frac{y}{r}$ .

$r = \frac{3}{\frac{y}{r}}$

Step 2

Multiply both sides by $r$ .

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Step 2.1

Multiply both sides by $r$ .

$r \cdot r = r \frac{3}{\frac{y}{r}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $r$ by $r$ .

$r^{2} = r \frac{3}{\frac{y}{r}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify $r \frac{3}{\frac{y}{r}}$ .

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Step 2.3.1.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.3.1.2

Rewrite using the commutative property of multiplication.

$r^{2} = 3 r \frac{r}{y}$

Step 2.3.1.3

Multiply $3 r \frac{r}{y}$ .

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Step 2.3.1.3.1

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

$r^{2} = r \frac{3 r}{y}$

Step 2.3.1.3.2

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

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

Step 2.3.1.3.3

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

$r^{2} = \frac{3 (r^{1} r)}{y}$

Step 2.3.1.3.4

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

$r^{2} = \frac{3 (r^{1} r^{1})}{y}$

Step 2.3.1.3.5

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

$r^{2} = \frac{3 r^{1 + 1}}{y}$

Step 2.3.1.3.6

Add $1$ and $1$ .

$r^{2} = \frac{3 r^{2}}{y}$

Step 3

Since $r^{2} = x^{2} + y^{2}$ , replace $r^{2}$ with $x^{2} + y^{2}$ and $r$ with $\sqrt{x^{2} + y^{2}}$ .

$x^{2} + y^{2} = \frac{3 (x^{2} + y^{2})}{y}$