Question

Use a half-angle identity to find the exact value of sinPi/8

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Answer:

  sin(π/8) = (1/2)√(2-√2)

Step-by-step explanation:

Using the half-angle formula ...

  $\sin{\dfrac{\theta}{2}}=\sqrt{\dfrac{1-\cos{\theta}}{2}}$

We can let θ = π/4 and simplify the result as follows:

  $\sin{\dfrac{\pi}{8}}=\sqrt{\dfrac{1-\cos{(\pi/4)}}{2}}=\sqrt{\dfrac{1-\dfrac{\sqrt{2}}{2}}{2}}=\sqrt{\dfrac{2-\sqrt{2}}{4}}\\\\=\boxed{\dfrac{1}{2}\sqrt{2-\sqrt{2}}}}$