How do you find the value of Csc(-8pi/6)?

1 Answer
Nghi N.
Oct 24, 2015

Find the value of csc (-(8pi)/6)

Ans: (2sqrt3)/3

Explanation:

csc (-(8pi)/6) = csc (-(4pi)/3) = 1/sin (-(4pi)/3).
First, find sin ((-4pi)/3)
sin ((-4pi)/3) = sin ((2pi)/3) = sqrt3/2 (co-terminal arcs).

csc ((-4pi)/3) = 1/(sin) = 2/sqrt3 = (2sqrt3)/3

Check by calculator.
sin ((-4pi)/3) = sin (-240^@) = 0.87
sin ((-4pi)/3) = sqrt3/2 = 1.73/2 = 0.87. OK

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