What are the coordinates of the North and South Poles?

Pre Calculus (converting coordinates)?

• 1. Express the Cartesian coordinates (3, - 4) as polar coordinates. 2. Express the Cartesian coordinates (0, 4) as polar coordinates. 3. Express the Cartesian coordinates (-square root 3/2 ,1/2 ) as polar coordinates. thank you for your help!

• Answer:

  1) x=3 y=-4 r=sqrt(x^2+y^2) r = sqrt [ (3)^2 +(-4)^2] = sqrt[9+16] = sqrt(25) = 5 r=5 θ = tan^-1(y/x) = tan^-1(-4/3) (3,-4) lies in quadrant IV ; tan is negative θ = -0.927 radians or -53.13 degrees (5, -0.927) is the polar coordiante 2) r= sqrt(x^2+y^2) = sqrt(0^2+4^2) = sqrt(16)=4 θ = tan^-1(4/0) = tan^-1(infinity) = pi/2 (4, pi/2) is the polar coordiante 3) r = sqrt[ 3/4 + 1/4] = sqrt(1) = 1 θ = tan^-1(-1/sqrt(3)) = -pi/6 (r, θ) = (1, -pi/6)