Question

I need help with this practice, having trouble solving it It is from my ACT prep guide

Answer 1

`\cos ((x)/(2))=\frac{\sqrt[]{30}}{10{}}`

Explanation:

Since the angle cosx=-2/5 is located in the third quadrant. Graph it and solve using the trigonometric ratios:

`\begin{gathered} \text{ Trigonometric identity:} \\ cos\mleft(x/2\mright)=\sqrt[]{(1+\cos x)/(2)} \end{gathered}`

Now, for the exact value of cos(x/2); substitute the given information:

`\begin{gathered} \cos ((x)/(2))=\sqrt[]{(1+(-(2)/(5)))/(2)} \\ \cos ((x)/(2))=\frac{\sqrt[]{30}}{10{}} \end{gathered}`