Question

Find the exact value by using a half-angle identity. sin 22.5degrees show your work. thanks!

Answer 1

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