How do you evaluate #csc ((4pi)/3)#?

1 Answer
Mar 13, 2018

#csc θ# is the same as #1/sin θ #

Explanation:

csc stands for cosec which is equivelant to #1/sin θ#.

The expression is thus equal to #1/sin((4 pi) / 3)#

Since we know by consulting the unit circle that #sin((4 pi) / 3) = -sqrt3/2# we get the expression #1/sin((4 pi) / 3) = 1/(-sqrt3/2)# which can be simplified to
#1/(-sqrt3/2)=2/(-sqrt3)=(-2sqrt3)/3#