If cos(α)=4/5 and we know that α∈(270˚; 360˚), how much is cos(α/2)?

1 Answer
Nov 3, 2017

cos(alpha/2)=-(3sqrt(10))/10

Explanation:

Using the identity:

cos^2(x/2)= 1/2(1+cosx)

cos(alpha/2)=sqrt(1+cosalpha)/sqrt(2)

If cosalpha=4/5

:.

cos(alpha/2)=(sqrt(1+4/5))/sqrt(2)=(sqrt(9/5))/sqrt(2)=(3/sqrt(5))/sqrt(2)=-(3sqrt(10))/10

Note:

Cosine is negative because alpha/2 is in the III quadrant and alpha is in the IV quadrant.