Question 973137: Find the magnitude and direction angle θ of the following vectors. Round the magnitude to the nearest tenth, and round the direction angle to the nearest degree, if rounding is necessary.
v = (-5, -2)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! if this vector starts at the origin, then you will get:
p1 = (0,0)
p2 = (-5,-2)
the x-coordinate of p2 is -5
the y-coordinate of p2 is -2
those coordinates form a right triangle with the origin.
the tangent of the angle of that triangle would be -2/-5.
tan^-1(2/5) = 21.80140949 degrees.
that's the reference angle of the triangle in quaedrant 3.
the angle in quadrant 3 is 180 + 21.80140949 = 201.80140949 degrees.
that's the direction.
the magnitude is sqrt((-2)^2 + (-5)^2) = sqrt(4+25) = sqrt(29).
the direction in quadrant 3 is generally in a south west direction.
since the reference angle is only 21 degrees, it's closer to west than south.
halfway south and halfway west would be an angle of 180 + 45 = 225 degrees.
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