Finding the value of alpha

Question

Given cos(alpha)=5/6 and alpha is in quadrant I, find the exact value of cos(alpha/2).
Note: You are not allowed to use decimals in your answer.

Answer 1

Using the half angle identity, cos(α/2) = ±√[(1+cosα)/2].  Since α lies in quadrant 1, so does α/2.  Therefore, cos(α/2) is positive.

 

So, cos(α/2) = √[(1+5/6)/2] = √[(11/6)/2]

 

                                            =√(11/12) = (11√12)/12 

 

                                                              = (22√3)/12

 

                                                              = (11√3)/6