1. Convert the following rectangular coordinates into polar coordinates.
(a) (-3.0)
(b) (-2√3, 2)
2. Convert the following polar coordinates into rectangular coordinates.
(a) (3, 5π/4)
(b) (4, 3π)
3. What is the radius and center of the circle r = -8sinθ?
4. Convert rcosθ = 4 to rectangular coordinates.
5. Convert 2xy = x2 + y2 to polar coordinates.
6. Find the parametric equations for the following lines:
a. The line y = 8x + 2 from x =1 to x =4.
b. The line from the point (-1,3) to {1,7).
7. When do the lines x = 2t, y = 1 +2t and x = 4-5s, y = -9 +2s intersect?
8. Find the parametric equations for the following curves:
(a) y = 1 -x2 for positive y.
(b) x2 + y2 = 14 with particle moving clockwise from (√14, 0) to (√14 , 0)
9. For the parametric curve given by x(t) = t4 - cos(t) and y(t) = e2t - t, determine dy/dx, d2y/dx2
10. Sketch the curve of the following parametric equations:
(a) x= sint, y = t, t ∈ R
(b) x =5t - 3, y = 7t - 2 where 0 ≤ t ≤ 1
(c) x= sin(2t), y = cos(2t) where 0 ≤ t ≤ π/2
11. Let a =< -3,0,4> and b =< -1,2,3 >
(a) Calculate -3a + 4b.
(b) Find a vector of length .6 in the opposite direction of a.
(c) Fid na a unit vector in the direction of b.
(d) Determine projb(a) and proja(b).