Question

Find the exact value by using a half-angle identity.

sin 22.5degrees
show your work. thanks!

Answer 1

`sin( ( \alpha )/(2))=\sqrt{ (1-cos\alpha)/(2) }\\\alpha=45^\circ\\ sin(22,5)=\sqrt{ (1-cos45)/(2) }\\ sin(22,5)=\sqrt{ (1-(\sqrt2)/(2))/(2) }\\ sin(22,5)=\sqrt{ (2-\sqrt2)/(2)*(1)/(2) }\\sin(22,5)=\sqrt{ (2-\sqrt2)/(4) }`