Unit Vector with Angle θ=-3∏/4 from Positive X-Axis

[shamus390]

Find the unit vector that makes an angle θ=-3∏/4 with the positive x-axis

I know to find a unit vector you divide the given vector by its magnitude, so I guess my problem is finding any vector that makes that angle with the positive x axis. I figured if that angle was the slope of a line, then when x=1, y=-3∏/4. So I divided the vector <1,-3∏/4> by its magnitude and got the wrong answer. Could someone point me in the right direction?

Thanks in advance.

 

[Char. Limit]

Well, first, y is not 3pi/4. Remember your equation for slope: tan(theta) = y/x. What's tan(theta) in this case? That'll give you y/x = c for some c, and you can use THAT to get a vector.

 

[HallsofIvy]

A unit vector that makes angle $\theta$ with the positive x-axis is $cos(\theta)\vec{i}+ sin(\theta)\vec{j}$. I thought everyone knew tha!

"I figured if that angle was the slope of a line"
No, the tangent of the angle is the slope of the line.