In which quadrant is the terminal of an angle in standard position whose measure is #(-55pi)/3#?

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Answer 1 · 2015-02-03T09:14:54

The answer is: #5/3pi#.

Every #2pi# the angles repeat. So it is possible to add, or subtract, at one angle #2pi# how many times you want.

Let's sum it until we "reach" an angle of "the first round", i.e until the angle is in #[0,2pi]#.

#-55/3pi+2pi=-55/3pi+6/3pir=-49/3pi#

#-49/3pi+6/3pi=-43/3pi#

#-43/3pi+6/3pi=-37/3pi#

#-37/3pi+6/3pi=-31/3pi#

#-31/3pi-6/3pi=-25/3pi#

#-25/3pi+6/3pi=-19/3pi#

#-19/3pi+6/3pi=-13/3pi#

#-13/3pi+6/3pi=-7/3pi#

#-7/3pi+6/3pi=-pi/3#

#-pi/3+6/3pi=5/3pi#.