Question

i need help with number 22.i have the formula cos theta/2 = plus or minus the square root of (1 + cos theta)/2 which i changed to cos beta/2 = plus or minus the square root of (1 + cos beta)/2.i put in -12/13 for cos beta and got: plus or minus the square root of (1/13)/2. i then did keep change flip and multiplied 1/13 • 1/2 and got 1/26. i’m stuck here and don’t know how to do the square root of 1/26

Answer 1

`cos\beta=-(12)/(13)`

Use the next identity to find cosβ/2:

`cos((\theta)/(2))=\pm\sqrt{(1+cos\theta)/(2)}`
`\begin{gathered} cos((\beta)/(2))=\pm\sqrt{(1+(-(12)/(13)))/(2)}=\pm\sqrt{(1-(12)/(13))/(2)}=\pm\sqrt{((13-12)/(13))/(2)}=\pm\sqrt{((1)/(13))/(2)}=\pm\sqrt{(1)/(26)}=\pm(√(1))/(√(26))=\pm(1)/(√(26)) \\ \\ Rationalize\text{ the denominator:} \\ \pm(1)/(√(26))*(√(26))/(√(26))=\pm(√(26))/(26) \end{gathered}`

Then, the cos(β/2) is ± √26 /26