Question

Half angle for sin (11pi/12) anyone?

Answer 1

\[\sin(11 \pi/12)=\sin(\pi-\pi/12)=\sin(\pi/12)=\sqrt{\frac{ 1-\cos(\pi/6) }{ 2}}\]and we know\[\cos(\pi/6)=\frac{ \sqrt{3} }{ 2 }\] then \[\sin(11 \pi/12)=\sqrt{\frac{ 2-\sqrt{3} }{ 4 }}=\frac{ \sqrt{2-\sqrt{3}} }{ 2 }=0.2588\]