half angle trigonometry formula

Question

given cos (a)=4/5 and 3pi/2<a<2pi. 

Find the exact value of cos (a/2)

 

Answer 1

cos(a) = 2cos²(a/2) - 1

Since a/2 in the second quadrant,

cos(a/2)

= -sqrt[(1/2)(1+cos(a))]

= -sqrt[(1/2)(1+4/5)]

= -3sqrt(10)/10 <==Answer