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Explore the concepts of polar coordinates through graphing techniques, symmetries, and special curves. Learn how to plot polar equations including circles, cardioids, and limacons. Understand the slope of tangents at poles and calculate areas and arc lengths of polar curves, including petals of roses and inner loops of shapes. This comprehensive overview provides examples and methodologies essential for mastering polar graphs and their applications in mathematics.
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11.4 – Graphing in Polar Coordinates Polar Symmetries
11.4 – Graphing in Polar Coordinates Polar Symmetries
11.4 – Graphing in Polar Coordinates Polar Symmetries
11.4 – Graphing in Polar Coordinates Slope of a Tangent for
11.4 – Graphing in Polar Coordinates Slope of a Tangent for When passes through the pole,and the slope of the tangent is:
11.4 – Graphing in Polar Coordinates Slope of a Tangent for Given the polar equation, find the polar coordinates and the slope of the tangent at • At
11.4 – Graphing in Polar Coordinates Polar Equations Basic Equations: A circle with its center at the pole. A line through the pole at the angle . Examples:
11.4 – Graphing in Polar Coordinates Polar Equations Plotting Polar Curves Example:
11.4 – Graphing in Polar Coordinates Polar Equations Plotting Polar Curves Example:
11.4 – Graphing in Polar Coordinates Special Polar Curves Limacon w/ a dimple Cardioid Circle Limacon w/ a loop
11.4 – Graphing in Polar Coordinates Special Polar Curves Spiral out Spiral in Roses Lemniscate Parabola
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve r
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Cardioid
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of entire region Area of a one petal Rose w/3 petals
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of a one petal Rose w/3 petals
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of the inner loop Limacon w/ a loop
11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of the region outside r = 2 and inside r = 4sin Need Pts. Of Intersection
11.5 – Area and Lengths in Polar Coordinates Calculate the area of the region outside , inside , and in the first quadrant. Points Of Intersection
11.5 – Area and Lengths in Polar Coordinates Arc Length of a Polar Curve
11.5 – Area and Lengths in Polar Coordinates Find the arc length of the polar curve between the given angle interval.
11.5 – Area and Lengths in Polar Coordinates Find the arc length of the polar curve between the given angle interval.
11.5 – Area and Lengths in Polar Coordinates Find the arc length of half of the inside loop
