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\text { Consider the polar curves } r=2 \cos (2 \theta) \text { and } r=1 \text {. } a) Sketch (by hand and only by hand) the two curves on the same graph. \text { b) Determine two angles } \theta \text { such that }-\frac{\pi}{4} \leq \theta \leq \frac{\pi}{4} \text {, where the two curves inter- } sect. You must find the angles algebraically and not from your sketch. c) Find the exact area of the region giving all the points that are inside the first curve and inside the second curve. Show all your work. (3 points)

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