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17 well call them w0 and w1 we get w0 4cis 23 22 0

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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 8 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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