Question

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

Answer 1

Let Ф = 22.5°

⇒2Ф = 45°

so cos(2Ф) = 1 - 2sin²Ф

⇒ cos 45 = 1 - 2 sin²(22.5)

⇒ 1/√2 = 1 - 2 sin²(22.5)

⇒ (1 - 1/√2)/2 = sin²(22.5)

⇒ sin²(22.5) = (√2 - 1)/2√2

⇒ sin (22.5) = √{(√2 - 1)/2√2}

⇒sin (22.5) = √{(2 - √2)}/2

or  $sin(22.5)=\frac{\sqrt{2-\sqrt{2}}}{2}$

Answer 2

Answer:

route 2 -2 is the answer