Question Number 185073 by emmanuelson123 last updated on 16/Jan/23
Answered by Frix last updated on 16/Jan/23
$$\mathrm{16}°\mathrm{52}'\mathrm{30}''\:=\:\frac{\mathrm{3}\pi}{\mathrm{32}} \\ $$$$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{8}}\:=\frac{\sqrt{\mathrm{2}+\sqrt{\mathrm{2}}}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\frac{{x}}{\mathrm{2}}\:=\sqrt{\frac{\mathrm{1}−\sqrt{\mathrm{1}−\mathrm{sin}^{\mathrm{2}} \:{x}}}{\mathrm{2}}} \\ $$$$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{16}}\:=\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}}{\mathrm{2}} \\ $$$$\mathrm{sin}\:\frac{\mathrm{3}\pi}{\mathrm{32}}\:=\frac{\sqrt{\mathrm{2}−\sqrt{\mathrm{2}+\sqrt{\mathrm{2}−\sqrt{\mathrm{2}}}}}}{\mathrm{2}} \\ $$