How do you convert x=3 into a polar equation?

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How do you convert x=3 into a polar equation?

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Answer 1 · 2016-04-22T12:17:59

$r = 3 sec θ$ $r=3 sec theta$ .

Explanation:

$x = r cos θ$ $x=r cos theta$
So, x =3 becomes $r cos θ = 3 or r = 3 sec θ$ $r cos theta = 3 or r = 3 sec theta$

x = 3 is the straight line parallel to y-axis, in the first and fourth quadrants, at a distance 3 from the y-axis.

The polar forms of lines parallel to the axes are $r = a sec θ, θ \in (- \frac{π}{2}, \frac{π}{2}) and r = a csc θ, θ \in (π, 0)$ $r = a sec theta, theta in (-pi/2, pi/2) and r = a csc theta, theta in (pi, 0)$ .
r ranges from $+ \infty$ $+oo$ down to a and increase to $+ \infty$ $+oo$ .

Unless necessitated (in problems relating to radial directions), polar forms are avoided for equations of straight lines . .

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How do you convert x=3 into a polar equation?

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