Answer:
[tex]\cos (\frac{x}{2})=\frac{\sqrt[]{30}}{10{}}[/tex]
Step-by-step explanation:
Since the angle cosx=-2/5 is located in the third quadrant. Graph it and solve using the trigonometric ratios:
[tex]\begin{gathered} \text{ Trigonometric identity:} \\ cos\mleft(x/2\mright)=\sqrt[]{\frac{1+\cos x}{2}} \end{gathered}[/tex]
Now, for the exact value of cos(x/2); substitute the given information:
[tex]\begin{gathered} \cos (\frac{x}{2})=\sqrt[]{\frac{1+(-\frac{2}{5})}{2}} \\ \cos (\frac{x}{2})=\frac{\sqrt[]{30}}{10{}} \end{gathered}[/tex]
