Question

If `cscx=2`, 90°<x<180° how do you find sin(x/2), cos(x/2), tan(x/2)?

Answer 1

`csc x = 1/sin x = 2 -> sin x = 1/2 -> x = (5pi)/6` (90 < x < 180)

`cos ((5pi)/6) = (-sqrt3)/2`

`2cos^2 (x/2) = 2cos^2 ((5pi)/12) = 1 + cos x = 1 - (sqrt3)/2 = 0.134`

`cos^2 ((5pi)/12) = 0.067` ->`cos((5pi)/12) = 0.26`

`sin x = sin ((5pi)/6) = 2.sin ((5pi)/12).cos ((5pi)/12)`

`1/2 = 2(0.26).sin (5pi/12)` -> `sin ((5pi)/12) = 1/1.04 = 0.96`