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Question Number 133851 by physicstutes last updated on 24/Feb/21

$$\mathrm{A}\mathrm{circle}\mathrm{of}\mathrm{radius}r\mathrm{is}\mathrm{such}\mathrm{that}\mathrm{it}\mathrm{subtends}\mathrm{an}$$$$\mathrm{angle}\mathrm{of}\alpha \mathrm{at}\mathrm{its}\mathrm{centre}.\mathrm{A}\mathrm{chord}\mathrm{cuts}\mathrm{the}\mathrm{circle}\mathrm{such}$$$$\mathrm{that}\mathrm{it}\mathrm{divides}\mathrm{the}\mathrm{circle}\mathrm{into}\mathrm{two}\mathrm{segments}\mathrm{of}\mathrm{areas}\mathrm{in}$$$$\mathrm{the}\mathrm{ratio}1:5.\mathrm{show}\mathrm{that}$$$$\sin \alpha =\alpha -\frac{\pi }{3}$$

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