12 m Given Sina And a IL FindCos 13 Solutionsin alpha 1213 o

12 ,m Given Sina And- a IL FindCos 13

sin alpha= 12/13

opposite=12 and hypotenuse=13

therefore adjacent=sqrt(169-144)=5

cos alpha=ajdacent/hypotenuse

And cos theta is negative in second quadrant

therefore cos alpha=-5/13

using half angle formula

cos²alpha/2= 1/2(1+cos alpha) = 1/2(1-5/13) = 1/2(8/13)=4/13

cos²alpha/2=4/13

Alpha is in second quadrant. Therefore alpha/2 is in first quadrant

And in first quadrant cos theta is positive

Therefore cos (alpha/2)=sqrt(4/13)= 2sqrt13/13