How do you evaluate $arcsin (-1/2)$ ?

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Answer 1 · 2015-06-09T18:43:49

find $arcsin (-1/2)$

$sin x = -1/2$ --> find x ?

Trig table gives:

$sin x = -1/2$ = sin (-30) = sin (360 - 30) = sin 330 -> x = 330 deg

Trig unit circle gives another arc x that has the same sin value $(-1/2)$ :

x = 180 + 30 = 210 deg

Within period (0, 360), there are 2 answers: 210 and 330 deg

How do you evaluate arcsin (-1/2)arcsin (-1/2)?