Eliminate the parameter to write the corresponding ...



Eliminate the parameter to write the corresponding rectangular equation. Be able to graph these:

1) x = t2 ( 4t + 3 2) x = 2cosθ + 2 3) x = 3tanθ + 1

y = t + 3 y = sinθ ( 5 y = 2secθ ( 4

t = y – 3 so [pic], y + 5 = sin ө [pic]

x = (y – 3)2 – 4(y – 3) + 3 [pic] [pic]

[pic] [pic] [pic]

4. Using the parametric equations [pic]

A. Complete a table: B. Plot the points (x, y) from the table to graph the parametric equations. (Use arrows to show the direction.

[pic]

5. Find two different sets of parametric equations for y = -7x4 ( 2x2 + 5

A. x = t B. x = t + 1

y = -7t4 ( 2t2 + 5 y = -7(t + 1)4 – 2( t + 1)2 + 5

6. [pic] A. Plot the given point on a polar graph.

B. Find four additional polar coordinates for the point 0 ≤ ( ≤ 2(.

C. Find the corresponding rectangular coordinates for the point.

A. B. C.

[pic]

Rectangular coordinates of a point are given. Find the polar coordinates.

7. (-2[pic], -2[pic]) 8. (-3, 0)

[pic] [pic]

Convert the rectangular equation to polar form.

9. x2 + y2 = 81 10. 4x ( 2y + 5 = 0

r = 9 4rcosө – 2rsinө = -5

[pic]

Convert the polar equation to rectangular equation in rectangular form.

11. [pic] 12. ( = [pic]

[pic] y = -x

Write the equation of the following polar graphs:

13. Limacon: ________________

14. Lemniscate: ______________

15. Rose: ________________

16. Circle: _____________

Name the polar graph that results from the following equations:

16. r = 3 + 3cos( _____________ cardioid

17. r = 4sin( ____________ circle with radius 2

18. r = 1 + 2sin( ______________ inner loop limacon

19. r = 2 + cos( ______________ convex limacon

Sketch 16 – 19.

Make sure you know how to find a maximum, zeros, and symmetry.

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|[pic] |[pic] |[pic] |0 |[pic] |[pic] |

|x | 2 |[pic] |3 |[pic] |2 |

|y | 1 | [pic] |0 | [pic] |1 |

[pic]

Arrows will show direction !

[pic]

[pic]

[pic]

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