Math 2414 Name: Polar Coordinates 1. (30 points) Sketch the graph of the curve 7' = sin 6+ cos 6', 0 S 6' S 11'. (a) Find the slopes of the tangent lines to the curve at each of the a: and yintercepts. (b) Find the Elvalues of all points on the graph where the tangent line is either vertical or horizontal, (c) Find the area of the region inside the curve and in the rst quadrant. 2. Sketch the graphs of the circle *3" = 3 cos Hand the cardioid r = 1 + cos Bin the same coordinate plane. Find the area. inside the circle but outside the cardioid. 3. Sketch the graph of the caIdioid \"r = 1 cos 6. (a) Find the area, of the region inside the graph. (b) Find the arc length of the graph