Q. 26 - Calculus

Question

Graph the equations in Exercises 25–32 in the polar plane. Compare your graphs with the corresponding graphs in Exercises 17–24 .

$r=\frac{1}{2}-\sin \theta$ 

Step-by-Step Solution

Answer

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Step 1: Identify the polar equation

Plot the polar equation by computing \(r\) for key values of \(\theta\) (0, \(\pi/6\), \(\pi/4\), \(\pi/3\), \(\pi/2\), etc.) and connecting the points.

Step 2: Compare with rectangular graph

The polar graph can be compared with the corresponding rectangular graph by noting how the radial distance \(r\) varies with angle \(\theta\).