Asked by Randy
What is the trigonmetric fact for sin 3.14/8?
Answers
Answered by
Reiny
I recognize your 3.14, most probably meant to stand for π
so you want sin π/8 or sin 22.5°
recall that cos 2A = 1 - 2sin^2 A
then cos 45° = 1 - 2sin^2 2.5°
2sin^2 22.5° = 1 - cos45° = 1 - √2/2
= (2 - √2)/2
sin^2 22.5 = (2 - √2)/4
sin 22.5 = sin π/8= √(2 - √2) / 2
so you want sin π/8 or sin 22.5°
recall that cos 2A = 1 - 2sin^2 A
then cos 45° = 1 - 2sin^2 2.5°
2sin^2 22.5° = 1 - cos45° = 1 - √2/2
= (2 - √2)/2
sin^2 22.5 = (2 - √2)/4
sin 22.5 = sin π/8= √(2 - √2) / 2