Let P be a point in the plane If P has polar coordinates r t

Let P be a point in the plane. If P has polar coordinates (r, theta) then it has rectangular coordinates (X, Y) where x = and y = If P has rectangular coordinates (X, Y) then it has polar coordinates (r, theta) where r^2 = and tan(theta) = Compare the polar equation of the circle r = 2 with its equation in rectangular coordinates. In which coordinate system is the equation simpler? Which coordinate system would you choose to study these curves? What about the rectangular equation of line Y = 2 compared to its polar equation? Which coordinate system would you choose to study lines?

Solution

a) x = r cos(theta) and y = r sin(theta)

b) r² =square root of (x² + y²) and tan(theta) = y /x

c) r = 2 will give a circle with radius 2 and origin as centre POLAR COORDINATE SYSTEM IS BEST TO STUDY CURVES

d) Y = 2 is a line parallel to X axis at a height of 2 units RECTANGULAR COORDINATE SYSTEM IS BEST TO STUDY STRAIGHT LINES