If (color(red)(x),color(blue)(y)) = (color(red)(-7sqrt(3)/2),color(blue)(7/2))
Then for an angle theta between the positive X-axis and the point (color(red)(x),co9lor(blue)(y)) with vertex at the origin,
by definition of tan
color(white)("XXXX")tan(theta) = (color(red)(-7sqrt(3)/2))/(color(blue)(7/2))
color(white)("XXXXXXXX")=-sqrt(3)
This value for tan(theta) is one found in the standard pi/3=6O^@ triangle
and tells us that the angle is either -pi/3 or 2pi/3
(color(red)(-7sqrt(3)/2),color(blue)(7/2)) is in Quadrant IV, so theta = -pi/3
The radius for the polar coordinate is given by the Pythagorean Theorem as
color(white)("XXXX")r=sqrt((color(red)(-7sqrt(3)/2))^2+(color(blue)(7/2))^2)
color(white)("XXXXX")=sqrt((color(red)(3*7^2)+color(blue)(7^2))/4
color(white)("XXXXX")=sqrt((cancel(4)*7^2)/cancel(4))
color(white)("XXXXX")=7
The Polar coordinate (theta,r) = (-pi/3,7)
