What does arcsin(cos ((-2pi)/3)) arcsin(cos(2π3)) equal?

2 Answers
Feb 26, 2016

-piπ/6

Explanation:

cos (-2piπ/3 ) = sin ( piπ/2 + (-2pi2π/3)) = sin (-))=sin(pi#/6)
arc sin (sin) is unit operator 1.

Feb 26, 2016

(7pi)/6 and (11pi)/6

Explanation:

On the trig unit circle,
cos ((-2pi)/3) = = cos (2pi)/3 = - 1/2cos(2π3)==cos(2π)3=12
sin x = -1/2sinx=12 --> arc x = - pi/6x=π6 and x = -(5pi)/6.x=5π6.
Answer using positive arcs (co-terminal arcs):
x = (7pi)/6x=7π6 and x = (11pi)/6x=11π6