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1. Determine the Cartesian coordinates of the points with polar coordinates (V2, - ). (0, 7), (-1, 400TT), and ( 2V/3, -32. Determine polar coordinates of the points with Cartesian coordinates (-1, 0), (3, v3), (-2, -2), and (1, 3. Sketch the graphs of the limacons: (a) r =2+ cose (b) r =1 + cose (c) r = 1 +2cose 4. Sketch the graph of the spiral of Archimedes: r = 0. 5. Convert the polar equation r = sind + cose to a rectangular equation. 6. Sketch the graph of the polar equation r = cos(20). 2 7. Convert the polar equation r = 3 sind + cos d to a rectangular equation.Polar Coordinates I Polar Coordinates of Points in the Plane In the x,y-plane (called the Cartesian plane), each point P is specified by an address consisting of two num- bers (a, b) which provide instructions on how to move from the origin of the plane to the point P. Thus (3,5) specifies a point reached by moving 3 units out on the positive x-axis, and then vertically 5 units. This is not the only way we could provide directions on how to reach P from the origin. In section 10.3 a second method is introduced. In this method we again use two numbers (r, 0) (called polar coordinates) to describe how to reach P. The first coordinate r, as for Cartesian coordinates, tells use where to move to on the x-axis. The second coordinate 0 specifies an angle. Here is how it works. Imagine that there is a string pinned at the origin (usually called the pole when we are using polar coordinates), and stretching out to the point r on the x-axis. Now rotate the string through an angle 8 (in the positive, counterclockwise, di- rection if 0 > 0, in the negative, clockwise, direction if 0