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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