How do you convert the polar coordinate (6, 2pi/3) into cartesian coordinates?

1 Answer
George C.
Aug 4, 2015

(x, y) = (r cos theta, r sin theta) = (6cos((2pi)/3), 6sin((2pi)/3))

= (6*-1/2, 6*sqrt(3)/2) = (-3,3sqrt(3))

Explanation:

Given radius r and angle theta, the cartesian coordinates x and y are given by the formulae:

x = r cos theta
y = r sin theta

Conversely, given x and y, the radius r and angle theta are determined by the formulae:

r = sqrt(x^2+y^2)
theta = "atan2"(y, x)

where "atan2"(y, x) is defined as follows:

"atan2"(y, x) = { (arctan(y/x), " if x > 0"), (arctan(y/x) + pi, " if x < 0 and y >= 0"), (arctan(y/x) - pi, " if x < 0 and y < 0"), (pi/2, " if x = 0 and y > 0"), (-pi/2, " if x = 0 and y < 0"), ("undefined", " if x = 0 and y = 0") :}

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