Question

Express the cartesian coordinates (0, 4) as polar coordinates.

Answer 1

The question is asking we convert from (x, y) coordinate to (r, theta) coordinates.  
So (0, 4) to (r, theta) 
 x = 0 and y = 4. 
 r = âš (x^2 + y^2)
 r = âš (0^2 + 4^2)
 r = âš (0 + 16)
 r = 4
 Also theta = tan^(-1)(x/y) = tan^(-1) (0/4) = 0
 So theta = 0
 Hence the (r, theta) coordinate is (4, 0)