Algebra Examples

$r = 4 \csc (x)$

Step 1

Simplify the right side.

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Step 1.1

Simplify $4 \csc (x)$ .

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Step 1.1.1

Rewrite $\csc (x)$ in terms of sines and cosines.

$r = 4 \frac{1}{\sin (x)}$

Step 1.1.2

Combine $4$ and $\frac{1}{\sin (x)}$ .

$r = \frac{4}{\sin (x)}$

Step 2

Multiply both sides by $r$ .

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Step 2.1

Multiply both sides by $r$ .

$r \cdot r = r \frac{4}{\sin (x)}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Multiply $r$ by $r$ .

$r^{2} = r \frac{4}{\sin (x)}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify $r \frac{4}{\sin (x)}$ .

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Step 2.3.1.1

Separate fractions.

$r^{2} = r (\frac{4}{1} \cdot \frac{1}{\sin (x)})$

Step 2.3.1.2

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$r^{2} = r (\frac{4}{1} \csc (x))$

Step 2.3.1.3

Rewrite using the commutative property of multiplication.

$r^{2} = \frac{4}{1} r \csc (x)$

Step 2.3.1.4

Divide $4$ by $1$ .

$r^{2} = 4 r \csc (x)$

Step 3

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

$x^{2} + y^{2} = 4 \sqrt{x^{2} + y^{2}} \csc (x)$