How do you determine the polar coordinates for the intersection point(s) of the following polar equations: $r = 1$ $r = 1$ and $r = 2 cos θ$ $r = 2 \cos \theta$ ?

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How do you determine the polar coordinates for the intersection point(s) of the following polar equations: $r = 1$ $r = 1$ and $r = 2 cos θ$ $r = 2 \cos \theta$ ?

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Answer 1 · 2015-01-12T13:42:44

You can substitute $r = 1$ $r=1$ in the second equation $r = 2 cos (θ)$ $r=2cos(theta)$ and you'll get:

$1 = 2 cos (θ)$ $1=2cos(theta)$ and
$cos (θ) = \frac{1}{2}$ $cos(theta)=1/2$
There are two angles with $cos$ $cos$ equal to $\frac{1}{2}$ $1/2$ ;
$theta_1=60°$ and $theta_2=300°$ .

The coordinates of your points are then:

$(1;60°)$ and $(1;300°)$

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How do you determine the polar coordinates for the intersection point(s) of the following polar equations: $r = 1$ $r = 1$ and $r = 2 cos θ$ $r = 2 \cos \theta$ ?

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How do you determine the polar coordinates for the intersection point(s) of the following polar equations: r = 1r=1r = 1 and r = 2 \cos \thetar=2cosθr = 2 \cos \theta?

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How do you determine the polar coordinates for the intersection point(s) of the following polar equations: $r = 1$ $r = 1$ and $r = 2 cos θ$ $r = 2 \cos \theta$ ?