Algebra Examples

$r \cos (x) = 4$

Step 1

Multiply both sides by $r$ .

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Step 1.1

Multiply both sides by $r$ .

$r (r \cos (x)) = r \cdot 4$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $r$ by $r$ by adding the exponents.

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Step 1.2.1.1

Move $r$ .

$r \cdot r \cos (x) = r \cdot 4$

Step 1.2.1.2

Multiply $r$ by $r$ .

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

Step 1.3

Simplify the right side.

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Step 1.3.1

Move $4$ to the left of $r$ .

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

Step 2

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

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