Angle x is a third quadrant angle such that cos x =−1/5.
What is the exact value of cos(x/2)?
Enter your answer, in simplest radical form, in the box.
cos(x/2) =
Trig identity cos ( x/2) = ± sqrt ( ( 1 + cosx)/2)
= ± sqrt (4/10)
=± 2 sqrt 10 /10
= ± 1/5 sqrt 10 = - 1/5 sqrt 10 (since original cos was in Q III x/2 is in Q II and is negative)