Angle x is a third quadrant angle such that cosx=−1/5 .
What is the exact value of cos(x/2) ?
Enter your answer, in simplest radical form, in the box.
cos(x/2) =
cos (x / 2) will be a Q2 angle if x is in Q3.....so....cos (x /2 ) is negative ...so
cos ( x / 2) = - √ [ ( 1 + cos x ) / 2 ] = - √ [ (1 - 1/5) / 2 ] = - √ [ 4 / 10] = - 2/ √ 10 =
- 2√ 10 / 10 =
- √ 10 / 5
