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11.4 – Graphing in Polar Coordinates

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.

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11.4 – Graphing in Polar Coordinates

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  1. 11.4 – Graphing in Polar Coordinates Polar Symmetries

  2. 11.4 – Graphing in Polar Coordinates Polar Symmetries

  3. 11.4 – Graphing in Polar Coordinates Polar Symmetries

  4. 11.4 – Graphing in Polar Coordinates Slope of a Tangent for

  5. 11.4 – Graphing in Polar Coordinates Slope of a Tangent for When passes through the pole,and the slope of the tangent is:

  6. 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

  7. 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:

  8. 11.4 – Graphing in Polar Coordinates Polar Equations Plotting Polar Curves     Example:

  9. 11.4 – Graphing in Polar Coordinates Polar Equations Plotting Polar Curves   Example: 

  10. 11.4 – Graphing in Polar Coordinates Special Polar Curves Limacon w/ a dimple Cardioid Circle Limacon w/ a loop

  11. 11.4 – Graphing in Polar Coordinates Special Polar Curves Spiral out Spiral in Roses Lemniscate Parabola

  12. 11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve  r

  13. 11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Cardioid

  14. 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

  15. 11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of a one petal Rose w/3 petals

  16. 11.5 – Area and Lengths in Polar Coordinates Area of a Polar Curve Area of the inner loop Limacon w/ a loop

  17. 11.5 – Area and Lengths in Polar Coordinates

  18. 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

  19. 11.5 – Area and Lengths in Polar Coordinates Calculate the area of the region outside , inside , and in the first quadrant. Points Of Intersection

  20. 11.5 – Area and Lengths in Polar Coordinates Arc Length of a Polar Curve

  21. 11.5 – Area and Lengths in Polar Coordinates Find the arc length of the polar curve between the given angle interval.

  22. 11.5 – Area and Lengths in Polar Coordinates Find the arc length of the polar curve between the given angle interval.

  23. 11.5 – Area and Lengths in Polar Coordinates Find the arc length of half of the inside loop

  24. 11.5 – Area and Lengths in Polar Coordinates

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