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

1 Answer
Feb 21, 2018

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

Explanation:

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)

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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