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A point (-3.5, -2.5) lies on the standard coordinate plane as the endpoint of a vector that starts at the origin and ends there. Find the angle that is formed by the vector in reference to the positive x-axis. Be sure to round to the nearest degree.


The answer is 216.

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2 solutions

The vector is clearly on the III quadrant, since its axes and ordinate are both negative. We can find the angle made by this vector with the negative x-axis by using tan 1 2.5 3.5 \tan^{-1}{\frac{-2.5}{-3.5}} which gives 35.5 4 o 35.54^o . Rounded to the nearest degree gives 3 6 o 36^o . Recall that the vectors is on the III quadrant, therefore the angle made by itself with the positive x-axis is equal 180 + 36 = 21 6 o 180+36=216^o

Jennifer Lin
Dec 26, 2013

A reference from the positive x is where the angle is 0 degrees. To find the angle that the vector forms with the x axis in general, simply do inverse tangent which will result in a 35.5 degree angle formed with the negative x. Adding 180 to it gives us the whole piece interested, and rounding it up gives us 216 Degrees

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