9.3 #33

I don't know, most of you probably already understand how to do this problem, but personally it tripped me up, so here's a solution.

You know the magnitude of v is 1/2 and the direction angle is 250degrees. It helped me to draw a right triangle in the third quadrant of a set of axes, with a hypotenuse of 1/2. Since the direction angle is 250 degrees, this means the hypotenuse makes an angle of 70degrees with the negative x-axis. I then labeled the horizontal leg "x" and the vertical leg "y" and said that cos(70)=x/(1/2) or cos(70)=2x and that sin(70)=y/(1/2) or sin(70)=2y. So x=cos70/2 and y=sin70/2. You can use a calculator to approximate these values, but don't forget to make each one negative, since they are in the third quadrant! The component form of the vector is thus <-.17101, -.469846>.