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#