Finding sin(1/2)x

This angle falls into the frist quadrant since both the cosine and tangent are positive

And r = sqrt (7^2 + 24^2)  = sqrt(625)  = 25

And cos (theta) = x / r = 7/25

So....using an identity

sin(theta / 2)  = sqrt (  [1 - cosx] 2 )  =  sqrt ( [1 - 7/25]/2)  = sqrt( [25 - 7] / 50)  =

sqrt [ 18/50]  = sqrt [ 9/25]  = 3/5