How do you evaluate arctan(-1) using a unit circle?

1 Answer
Apr 21, 2015

Using a unit circle centered at (0,0) in the Cartesian plane
tan(theta) is the y coordinate value divided by the x coordinate value of the intersection of the unit circle and a ray extending from the origin at an angle of theta

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Asking for arctan(-1) is the same as asking to solve
for theta in
tan(theta) = -1

This will happen when x and y have equal magnitudes but opposite signs
Within the domain theta epsilon [0,2pi]
this only happens at
theta = (3pi)/4
and
theta = (7pi)/4