# Trig: Angles of Vectors

1. May 5, 2010

### k_squared

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|| = $$\sqrt{}$$(9+9) = 3$$\sqrt{}$$2
a1 = 3$$\sqrt{}$$2 * cos theta

=1/$$\sqrt{}$$2 =acos = 45 degrees.

However doing the other side of the equation...

a2= -1/$$\sqrt{}$$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. May 5, 2010

### 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.