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

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Answer 1 · 2015-05-30T03:37:39

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

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

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

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

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

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

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