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Question Number 35362 by 26488679 last updated on 18/May/18

Commented by 26488679 last updated on 18/May/18

$$isarcsin(-\frac{1}{2})canbeequalto210°?$$

Commented by ajfour last updated on 18/May/18

$$notaprincipalvalue.$$

Commented by prof Abdo imad last updated on 18/May/18

$$wehavearcsin(-\frac{1}{2})=-\frac{\pi }{6}andarcsin\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi }{3}$$$$\Rightarrow sin\{arcsin(-\frac{1}{2})+2arcsin\left(\frac{\sqrt{3}}{2}\right)\}=$$$$sin(-\frac{\pi }{6}+\frac{2\pi }{3})=sin\left(\frac{3\pi }{6}\right)=sin\left(\frac{\pi }{2}\right)=1answerD$$

Answered by ajfour last updated on 18/May/18

$$\sin (-\frac{\pi }{6}+2\times \frac{\pi }{3})=\sin \frac{\pi }{2}.$$

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