Consider the polar equation we are investigating over different intervals of theta. We are considering the following equation as theta goes from 0 to 2pi:
When a, b, and k are all equal to 1, the graph of our equation looks like this:
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What would happen if our angle theta was over a different interval?
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Notice that for our graph to be closed, theta must follow a similar period as the cosine function, from 0 to 2pi.