How do you convert $r = - 3 sec θ$ $r=-3sectheta$ into rectangular equations?

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Answer 1 · 2016-07-15T06:00:43

$x = - 3$ $x = -3$

Knowing that $x = r cos (θ)$ $x = r cos(theta)$ and $y = r sin (θ)$ $y = r sin(theta)$ , we can start off by rewriting our polar equation:

$r = - 3 sec (θ) = - 3 \cdot \frac{1}{cos (θ)}$ $r = -3sec(theta) = -3 * (1)/(cos(theta))$ , so then

$r = - \frac{3}{cos (θ)}$ $r = -3/cos(theta)$

Multiplying both sides by $cos (θ)$ $cos(theta)$ gives us

$r cos (θ) = - 3$ $r cos(theta) = -3$

Substituting $x$ $x$ for $r cos (θ)$ $r cos(theta)$ , since $x = r cos (θ)$ $x = rcos(theta)$ we get

$x = - 3$ $x = -3$

How do you convert r=-3secthetar=−3secθr=-3sectheta into rectangular equations?