Algebra Examples

$x = y$

Step 1

Since $x = r \cos (θ)$ , replace $x$ with $r \cos (θ)$ .

$r \cos (θ) = y$

Step 2

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

$r \cos (θ) = r \sin (θ)$

Step 3

Solve for $r$ .

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Step 3.1

Subtract $r \sin (θ)$ from both sides of the equation.

$r \cos (θ) - r \sin (θ) = 0$

Step 3.2

Factor $r$ out of $r \cos (θ) - r \sin (θ)$ .

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Step 3.2.1

Factor $r$ out of $r \cos (θ)$ .

$r (\cos (θ)) - r \sin (θ) = 0$

Step 3.2.2

Factor $r$ out of $- r \sin (θ)$ .

$r (\cos (θ)) + r (- 1 \sin (θ)) = 0$

Step 3.2.3

Factor $r$ out of $r (\cos (θ)) + r (- 1 \sin (θ))$ .

$r (\cos (θ) - 1 \sin (θ)) = 0$

Step 3.3

Rewrite $- 1 \sin (θ)$ as $- \sin (θ)$ .

$r (\cos (θ) - \sin (θ)) = 0$

Step 3.4

Divide each term in $r (\cos (θ) - \sin (θ)) = 0$ by $\cos (θ) - \sin (θ)$ and simplify.

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Step 3.4.1

Divide each term in $r (\cos (θ) - \sin (θ)) = 0$ by $\cos (θ) - \sin (θ)$ .

$\frac{r (\cos (θ) - \sin (θ))}{\cos (θ) - \sin (θ)} = \frac{0}{\cos (θ) - \sin (θ)}$

Step 3.4.2

Simplify the left side.

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Step 3.4.2.1

Cancel the common factor of $\cos (θ) - \sin (θ)$ .

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Step 3.4.2.1.1

Cancel the common factor.

$\frac{r (\cos (θ) - \sin (θ))}{\cos (θ) - \sin (θ)} = \frac{0}{\cos (θ) - \sin (θ)}$

Step 3.4.2.1.2

Divide $r$ by $1$ .

$r = \frac{0}{\cos (θ) - \sin (θ)}$

Step 3.4.3

Simplify the right side.

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Step 3.4.3.1

Divide $0$ by $\cos (θ) - \sin (θ)$ .

$r = 0$