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Algebra/Trig : polar and rectangular coordinates

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Question
Don't really know much about trig, even though it's an algebra 2 class. I'm still required to do it. I'm trying to cross check with the answers I have.  From what I do know.

1.the magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 140, bearing 160
v: magnitude 200, bearing 290
w: u + v
  w: (282, 141)      w: (23603, 226)
  w: (153.6, 246)   w: (22, 182)


2.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 30, bearing 215
v: magnitude 30, bearing 110
w: 3u - v
  w: (17, 149)      w: (102, 231.5)
  w: (193, 232)      w: (29, 185)


3.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 10, bearing 30
v: magnitude 25, bearing 120
w: 8u + 3v
  w: (99, 56)      w: (110, 73)
  w: (312, 63)      w: (890, 42)
4.   
The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u:  magnitude 15, bearing 60
v:  magnitude 20, bearing 160
w:  2u - 3v
  w: (35, 110)      w: (71.6, 4.5)
  w: (4.5, 71.6)      w: (52.0, 260)


5.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 136, bearing 220
v: magnitude 197, bearing 300
w: u + v
  w: (258.1, 268.7)      w: (268.7, 258.1)
  w: (55.2, 223.4)      w: (223.4, 55.2)


6.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 218, bearing 22
v: magnitude 170, bearing 112
w: u - v
  (133.2, 72)      (72, 133.2)
  (276, 344.1)      (344.1, 276)
7.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 136,. bearing 220
v: magnitude 197, bearing 300
w: 2u - v
  (223, 104)      (104, 223)
  (180.8, 307)      (307, 180.8)


8.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 1850, bearing 125
v: magnitude 2960, bearing 25
w: u + 2v

  (5888, 43.0)      (43, 5888.0)
  (345, 22.2)      (22, 354.2)


9.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 460, bearing 0
v: magnitude 712, bearing 130
w: u + v
  (90, 545)      (545, 90)
  (220, 30)      (30, 220)


10.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitde 23, bearing 215
v: magnitude 14.5, bearing 105
w: u + v
  (22.7, 77)      (77, 22.7)
  (22.6, 177.9)      (177.9, 22.6)


11.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 3.62, bearing 25
v: magnitude 14.5, bearing 105
w: u + v
  (15.5, 92.1)      (92.1, 15.5)
  (22.4, 19.8)      (19.8, 22.4)


12.   The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 621, bearing 305
v: magnitude 336, bearing 15
3(w + u) = 2(w - v)
  (2190, 141.8)      (141.8, 2190)
  (225.6, 55)      (55, 225.6)

13.   Give the rectangular coordinates: (4, 30)
  (2√3, 2)      (2, 2√3)
  (3√2, 2)      (2, 3√2)


14.   Give the rectangular coordinates: (2, 45)
  (√5, √5)      (√3, √3)
  (√2, √2)      (2, 2)

Answer
I could pick the right answer for many of them by just drawing them on a graph.  
1) 153.6, 246 deg
2) 102, 231.5 deg
3) 110, 73 deg
4) 71.6, 4.5 deg
5) 258.1, 268.7 deg
6) 276, 344.1 deg
7) 307, 180.8 deg
8) 5888, 43 deg
9) 545, 90 deg
10) 22.6, 177.9 deg
11) 15.5, 92.1 deg
12) 2190, 141.8 deg
13) 2(3^1/2), 2
14) 2^1/2, 2^1/2

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