Question 438552
If Ɵ is in quadrant IV and sin Ɵ= -2/3 find the exact value of cos(Ɵ/2)
..
sinx=-2/3
cos^2x=1-sin^2x=1-4/9=9/9-4/9=5/9
cosx=sqrt(5/9)=sqrt(5)/3=.74536
Trig identity for cos (x/2) (half-angle formula)
cos(x/2)=+-sqrt((1+cosx)/2))  (use + value since cos is + in quadrant IV)
             =sqrt((1+.74536)/2))
             =sqrt(.87268)
             =.93417 
ans:
cos(x/2)=.93417