Question 1206661
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Place yourself at the origin. Face directly east.


Rotate 360 degrees clockwise and you'll still face east. 
The clockwise rotation is due to theta being negative.
Rotate another 30 degrees clockwise to aim along the vector that tutor Edwin has drawn.
This is in quadrant 4 which is the southeast quadrant.
Note how angles -390 and -30 are coterminal. 


If r > 0 was the case, then we'd walk from the origin 4 units in the direction vector Edwin has shown.
However, because r < 0 instead, we must walk 4 units in the complete opposite direction. 
Think "negative = opposite". 


This will mean the answer vector should point in the northwest quadrant (aka quadrant 2).
This is when x < 0 and y > 0.


r = -4
theta = -390


x = r*cos(theta) and y = r*sin(theta)
x = -4*cos(-390) and y = -4*sin(-390)
x = -4*cos(-30) and y = -4*sin(-30)
x = -4*cos(30) and y = 4*sin(30)
x = -4*( sqrt(3)/2 ) and y = 4*(1/2)
x = -2*sqrt(3) and y = 2


The answer in < x, y > form would be <font color=red>< -2*sqrt(3), 2 ></font>


This would be equivalent to writing <font color=red>-2*sqrt(3)*i + 2j</font> where i,j are the unit vectors pointing along the positive x axis and y axis respectively.
i = <1,0>
j = <0,1>


Edwin has the right idea, but needs to do a sign flip for the x and y components.
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