How do I graph cardioid #r = a(1-cosθ)#?
Calculate the desired number of data points, and put them on an appropriate graph paper.
ANY graphing or plotting must start with a table of values of the independent variable and the evaluated expression. With those values you may plot them on graph paper manually, or use a computer plotting program. Polar coordinate paper may make this easier for equations in polar coordinates.
Because polar coordinates are based on angles, unlike Cartesian coordinates, polar coordinates have many different ordered pairs. Because infinitely many values of theta have the same angle in standard position, an infinite number of coordinate pairs describe the same point. Also, a positive and a negative co-terminal angle can describe the same point for the same radius, and because the radius can be either positive or negative, you can express the point with polar coordinates in many ways.