How do you evaluate $csc((-321pi)/3))$ ?

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Answer 1 · 2015-06-23T18:35:56

- $oo$

Write $csc(-321pi/3)$ = -csc $107pi$ = -csc ( $106pi +pi$ )

$106 pi$ = $53 (2pi)$ =0

Hence -csc $107pi$ = -csc $pi$ = - $oo$

Answer 2 · 2015-06-24T03:02:37

Find $csc ((-321pi)/3)$

Call $((-321pi)/3) = x$

$sin x = sin (-107pi) = sin (-pi - (53)2pi) = sin (-pi) = 0$

Therefor $csc x = 1/sin x = 1/0$ -> undefined

How do you evaluate csc((-321pi)/3))csc((-321pi)/3))?