Trig
posted by Briana on .
How do i find the exact value of sin 15 using the half angle formula

sin (30/2) = +/ sqrt [(1cos 30)/2]
+ in first quadrant
= sqrt [ (1  {sqrt 3}/2)/2) ]
= sqrt [ (2  sqrt 3)/4 ]
= (1/2) sqrt (2  sqrt 3) 
use
cos 2A = 1  2sin^2 A
cos 30° = 1  2sin^2 15°
√3/2 = 1 2sin^2 15°
2sin^2 15°  1  √3/2 = (2√3)/2
sin^2 15° = (2√3)/4
sin 15° = √(2√3) /2
it would have been easier to do
sin15°
= sin(45°30°)
= sin45cos30  cos45sin30
= (√2/2)(√3/2) (√2/2)(1/2)
= (√6  √2)/4 which yields the same result as above