How do you evaluate #csc((17pi)/3)#?

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How do you evaluate #csc((17pi)/3)#?

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Answer 1 · 2016-12-23T14:16:48

#- (2sqrt3)/3#

Explanation:

#csc ((17pi)/3) = 1/sin ((17pi)/3)#.
Find #sin ((17pi)/3)# by using trig table and unit circle:

#sin ((17pi)/3) = sin (-pi/3 + (18pi)/3) = sin (-pi/3 + 6pi) = = sin (-pi/3) = - sin (pi/3) = - sqrt3/2#
There for:
#csc ((17pi)/3) = - 2/sqrt3 = - (2sqrt3)/3#

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How do you evaluate #csc((17pi)/3)#?

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