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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