380 Words2 Pages

Math Analysis Conics, Polar, Vectors, and Parametric Equations Review
Plot each point given in polar coordinates.
1. 2. 3.
Plot each point given in polar coordinates, and find other polar coordinates of the point for which a) b. c.
4. 5.
For each pair of points below, find the rectangular coordinates.
6. 7. 8.
For each pair of rectangular coordinates, find the polar coordinates.
9. (-3, -3) 10.
Write each equation in polar form.
11. 12. 2xy = 1 13. y = -3
Write each equation using rectangular coordinates (x, y).
14. 15.
Transform each polar equation to an equation in rectangular coordinates. Then identify and graph the equation.
16. 17. 18.
Identify and graph each polar equation.
19. 20.
Use the vectors in the figure at the right to graph each of the following vectors.
21. u + v
22. 2u – 3w
23. v - u
The vector, v, has an initial point P and terminal point Q. Write v in the form ai + bj.
24. P = (-3, 2) ; Q = (6, 5) 25. P = (-1, 4): Q = (6, 2)
Given v = 2i – 3j and w = -4i +2j, find the following.
26. 3v – 2w 27. 28.
Find the unit vector that has the same direction as v.
29. v = -3j 30. v = 2i – j
Given v= 3i + 2j and w = -5i – 7j, find:
31. 32.
Graph the curve whose parametric equations are given and show its orientation. Find the rectangular equation of each curve.
33. 34.
35. x = 2cos t, y = sin t;
36. Suppose that Adam throws a tennis ball off a cliff 300 meters high with an initial speed of 40 meters per second at an angle of 45 degrees to the horizontal.
a. Find parametric equations that describe the position of the ball as a function of time.
b. How long is the ball in the air?
c.

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