Write out the equation given
[tex]\cos 2x=-0.123[/tex]Solving for x as shown below
[tex]\begin{gathered} \cos 2x=-0.123 \\ 2x=\cos ^{-1}(-0.123) \\ 2x=-(82.93^0) \end{gathered}[/tex]Note that cosine is always negative in the second and third quadrant
The value of 2x in the second quadrant would be
[tex]\begin{gathered} 2x\text{ in the second quadrant is} \\ 2x=180^0-82.93^0 \\ 2x=97.07 \\ x=\frac{97.07}{2} \\ x=48.535^0 \end{gathered}[/tex]The value of 2x in the third quadrant would be
[tex]\begin{gathered} 2x\text{ in the third quadrant is} \\ 2x=180^0+82.93^0 \\ 2x=262.93 \end{gathered}[/tex][tex]\begin{gathered} 2x=262.93 \\ x=\frac{262.93}{2} \\ x=131.465^0 \end{gathered}[/tex]Hence, the values of x are 48.535° and 131.465°
