Given cosx = -12/13, pi<x<3pi/2, find the vaue of tan (x/2) ???

Question

When i do this question i get -i are an answer...and i'm sure the answer cannot be a complex number!! help?? please!

Answer 1

pi/2 < x/2 < 3pi/4
cosx = 2 cos^2 (x/2) -1 = -12/13
=> cos^2 (x/2) = 1/26 => cos(x/2) = +-1/(square root of 26)
cosx = 1- 2sin^2 (x/2) = -12/13
=> sin^2 (x/2) = 25/26 => sin(x/2) = 5/(square root of 26)
tan(x/2) = sin(x/2) / cos(x/2) = +-5

Answer 2

The steps are as follows:

cos(x) = -12/13

=> x = cos`1(-12/13) = 2.7468 radians

which is within the defined range.

x/2 = 1.3734

=> tan(x/2) = 5

Therefore the answer is '5'.

Answer 3

Evaluate sinx:
1-(-12/13)^2=25/169,
so
sin^2 x=25/169. Since sinx is negative in this quadrant,
sinx=-5/13.
Now use
tan(x/2)=sinx/(1+cosx)