How do you find the points of intersection of $theta=pi/4, r=2$ ?

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Answer 1 · 2018-02-21T15:54:06

Their point of intersection is at $x=sqrt2$ and $y=sqrt2$

$theta = pi/4$ is a ray emerging from the origin with an angle of $pi/4$ from the positive $x$ -axis. (cyan)

$r=2$ is a circle of radius 2 centered at the origin. (magenta)

Drawn with Graphmatica

The point of intersection in polar coordinates is (unsurprisingly)

$(r,theta) = (2,pi/2)$

To get the cartesian coordinates, apply the following

$x = rcos theta = 2 cos(pi/2) = 2 (1/sqrt2) = sqrt2$
$y = rsin theta = 2 sin(pi/2) = 2 (1/sqrt2) = sqrt2$

How do you find the points of intersection of theta=pi/4, r=2theta=pi/4, r=2?