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

1 Answer
Alan P.
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#

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