Expert: Sherry Wallin - 11/13/2009

Question
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
8. The magnitude and direction of vectors u and v are given. Find vector w's polar coordinates.
u: magnitude 1850, bearing 125°
w: u + 2v
v: magnitude 2960, bearing 25°
14. Give the rectangular coordinates: (2, 45°)
15.Give the rectangular coordinates: (-3, 120°)
16. Give the rectangular coordinates: (-5, 135°).
17. Give the rectangular coordinates: (7, -60°).
18. Give the rectangular coordinates: (-6, -150°).
19. Give the rectangular coordinates: (-3, -120°).
20. Give the polar coordinates: (4, 0).
22. Give the polar coordinates: (0, -3).
28. Write in x + yi form: 2.2(cos 150° + i sin 150°)
29. Write in x + yi form: 3(cos20° + i sin20°)
30.Write in x + yi form: 0.8(cos 250° + i sin 250°)  

Answer
Choose a few questions or I will address a couple. This site (as far as I am concerned) is for learning and not for providing an answer key. I am a teacher and that is the service I choose to provide. It is also helpful if you show how you are attempting to work the problems out so I can help you where you are having problems otherwise it is like the blind leading the blind. Now with that said here are a couple explained:

28. Write in x + yi form: 2.2(cos 150° + i sin 150°): the cos 150 deg is the same as the cos 30 deg except for the sign and the sin 150 deg is the same as the sin 30 including the sign. Cos 30 deg is sqrt3/2 and so for cos 150 deg it is -sqrt3/2 while the sin 30 deg = sin 150 deg = 1/2, thus your answer is (2.2)-sqrt3/2 +(2.2(1/2)i = -1.1sqrt3 + 1.1i

14. Give the rectangular coordinates: (2, 45°): 2 is the magnitude (r) and both the sine and the cosine of 45 deg is sqrt2/2 so x = r*cos 45 and y = r*sin 45 so (2,45°) = (sqrt2, sqrt2)
note 2*sqrt2/2 = sqrt2

Math Prof