Answer:
sin(π/8) = (1/2)√(2-√2)
Step-by-step explanation:
Using the half-angle formula ...
[tex]\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}[/tex]
We can let θ = π/4 and simplify the result as follows:
[tex]\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}[/tex]
