1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Trig: Angles of Vectors

  1. May 5, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the magnitude of a and the smallest positive angle theta from the positive x-axis to the vector OP that corrosponds to a.

    a= (3,-3)

    2. Relevant equations

    a1 = ||a|| * cos theta
    a2 = ||a|| * sin theta
    3. The attempt at a solution

    ||a|| = [tex]\sqrt{}[/tex](9+9) = 3[tex]\sqrt{}[/tex]2
    a1 = 3[tex]\sqrt{}[/tex]2 * cos theta

    =1/[tex]\sqrt{}[/tex]2 =acos = 45 degrees.

    However doing the other side of the equation...

    a2= -1/[tex]\sqrt{}[/tex]2 = asin = -45 degrees = 315 degrees, which is the right answer. I thought they were supposed to be consistent...
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 5, 2010 #2


    Staff: Mentor

    arccos produces an angle between 0 and 180 degrees, while arcsin produces an angle between -90 and + 90 degrees. Since your vector is in the fourth quadrant, an angle of 45 degrees wouldn't be right, nor would -45 degrees, since the problem asks for a positive angle.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook