Sin A= 5/13 find cos A/2

Answer 1

draw a right triangle

sinA=5/13

5 is the opposite leg and 13 is the hypotenuse

13^2=5^2+n^2

169-25=n^2

144=n^2

n=12, the adjacent leg

therefore cosA=12/13

cos(A/2)=±√([1+cosA]/2)

cos(A/2)=±√([1+12/13]/2)

cos(A/2)=±√([25/13]/2)

cos(A/2)=±√(25/26)

cos(A/2)=±√25/√26

cos(A/2)=±5/√26

cos(A/2)=±5√26/26