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Unformatted text preview: -plane A few remarks are in order. First, there is no relation, in general, between the period of the
function f (θ) and the length of the interval required to sketch the complete graph of r = f (θ) in
the xy -plane. As we saw on page 799, despite the fact that the period of f (θ) = 6 cos(θ) is 2π , we
sketched the complete graph of r = 6 cos(θ) in the xy -plane just using the values of θ as θ ranged
from 0 to π . In Example 11.5.2, number 3, the period of f (θ) = 5 sin(2θ) is π , but in order to obtain
the complete graph of r = 5 sin(2θ), we needed to run θ from 0 to 2π . While many of the ‘common’
polar graphs can be grouped in to families,9 the authors truly feel that taking the time to work
through each graph in the manner presented here is the best way to not only understand the polar
In this case, we could have generated the entire graph by using just the plot r = 4 cos(2θ), but graphed over
the interval [0, 2π ] in the θr-plane. We leave the details to the r...
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