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Equations of Polar Curves and Graphs: A Comprehensive Review Guide

This document contains a set of problems focused on polar coordinates and graphs, designed to enhance understanding of rose curves, circles, limacons, and cardioids. Each problem requires writing equations, converting between polar and rectangular coordinates, and involves graphing various shapes based on specified conditions. Problems include the creation of rose curves with petals, circles positioned at the origin, and limacons with specific intercepts, providing a thorough exploration of the relationships between polar and Cartesian equations.

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Equations of Polar Curves and Graphs: A Comprehensive Review Guide

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  1. Risk Review Game Polar coordinates and graphs (6.4, 6.5)

  2. Alex's Proof Tuesday, September 29, 2009 11:18 AM Problem 1 • Write the equation of a rose with 4 petals of length 2 with the first petal lying on the positive x-axis.

  3. Alex's Proof Tuesday, September 29, 2009 11:18 AM Problem 1 • Write the equation of a rose with 4 petals of length 2 with the first petal lying on the positive x-axis.

  4. Problem 2 • Write the equation of a circle centered at the origin (pole) with a diameter of 8.

  5. Problem 2 • Write the equation of a circle centered at the origin (pole) with a diameter of 8.

  6. Problem 3 • Write the equation of a limacon with an inner loop lying on the negative y-axis with x-intercepts of 2 and -2 and y-intercepts of 0, -2, and -6.

  7. Problem 3 • Write the equation of a limacon with an inner loop lying on the negative y-axis with x-intercepts of 2 and -2 and y-intercepts of 0, -2, and -6.

  8. Problem 4 • Write the equation of a circle lying on the negative x-axis with diameter of 8 and one of the endpoints is on the pole.

  9. Problem 4 • Write the equation of a circle lying on the negative x-axis with diameter of 8 and one of the endpoints is on the pole.

  10. Problem 5 • Write the equation of a limacon with no inner loop lying on the positive y-axis, x-intercepts of 5 and -5, and y-intercepts of 8 and -2.

  11. Problem 5 • Write the equation of a limacon with no inner loop lying on the positive y-axis, x-intercepts of 5 and -5, and y-intercepts of 8 and -2.

  12. Problem 6 • Write the equation of a cardioid with a length of 8 lying on the negative x-axis.

  13. Problem 6 • Write the equation of a cardioid with a length of 8 lying on the negative x-axis.

  14. Problem 7 • Convert (-3, 5) to polar coordinates. Round to the hundredths.

  15. Problem 7 • Convert (-3, 5) to polar coordinates. Round to the hundredths.

  16. Problem 8 • Convert to rectangular coordinates (EXACT ANSWER!).

  17. Problem 8 • Convert to rectangular coordinates (EXACT ANSWER!).

  18. Problem 9 Graph the following:

  19. Problem 9 Graph the following:

  20. Problem 10 • Graph the following:

  21. Problem 10 • Graph the following:

  22. Problem 11 • Graph the following:

  23. Problem 11 • Graph the following:

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