How do you change the polar equation $θ + \frac{π}{3} = 0$ $theta+pi/3=0$ into rectangular form?

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How do you change the polar equation $θ + \frac{π}{3} = 0$ $theta+pi/3=0$ into rectangular form?

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Answer 1 · 2017-01-04T03:56:28

$θ$ $theta$ is a constant, $- \frac{π}{3}$ $-pi/3$ , but r is allowed to be any value from $- \infty to \infty$ $-oo" to "oo$ ; this defines a line. Substitute ${tan}^{- 1} (\frac{y}{x})$ $tan^-1(y/x)$ for $θ$ $theta$ and then solve for the resulting line.

Explanation:

Given: $θ + \frac{π}{3} = 0$ $theta + pi/3 = 0$

Subtract $\frac{π}{3}$ $pi/3$ from both sides:

$θ = - \frac{π}{3}$ $theta = -pi/3$

Substitute ${tan}^{- 1} (\frac{y}{x})$ $tan^-1(y/x)$ for $θ$ $theta$ :

${tan}^{- 1} (\frac{y}{x}) = - \frac{π}{3}$ $tan^-1(y/x) = -pi/3$

Use the tangent function on both sides:

$\frac{y}{x} = tan (- \frac{π}{3})$ $y/x = tan(-pi/3)$

Multiply both sides by x:

$y = tan (- \frac{π}{3}) x$ $y = tan(-pi/3)x$

Here is a graph of the function:

![Desmos.com]( useruploads.socratic.org )

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How do you change the polar equation $θ + \frac{π}{3} = 0$ $theta+pi/3=0$ into rectangular form?

1 Answer

Explanation:

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