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