What is the reference angle for #(14pi)/3#?

1 Answer
Apr 30, 2015

It is always possible to add, or subtract, #2pi# to an angle to obtain an equivalent one. The symbol #-=# in the following passages is not a real #=#, but only an equivalent symbol.

#14/3pi-2pi -= 8/3pi -= 8/3pi-2pi -= 2/3pi#.

#2/3pi# is just #pi/3# less that #pi# so the acute angle (the reference angle) between #2/3 pi# and the horizontal is #pi/3#

Because they are coterminal, the reference angle for #14/3pi# is the same. It is #pi/3#.