Final answer:
To sketch the polar equation r = 2 / sin2θ, calculate a set of points by choosing various θ values and plot them in accordance with the relationship between polar and Cartesian coordinates. Note that r approaches infinity as θ approaches multiples of π.
Step-by-step explanation:
To sketch the graph of the polar equation r = 2 / sin2θ, we first need to understand how polar coordinates work. In a polar coordinate system, each point on a plane is determined by a distance r from the origin and an angle θ from the positive x-axis. The relationship between polar and Cartesian coordinates is given by x = r × cosθ and y = r × sinθ. To sketch the given polar equation, we can generate a set of points by choosing different values of θ and calculating the corresponding r value.
We should also consider the behavior of the function as θ approaches multiples of π, as the sine function will approach zero and the value of r will tend towards infinity. Due to the symmetrical properties of the sine function, this polar graph will have symmetry across the y-axis.