If cosθ = 7/25 and θ is acute, then cos(θ/2) equals:

The half-angle form is cos(θ/2) = √((1 + cosθ)/2) = √((32/25)/2) = √(16/25) = 4/5, the positive root because θ/2 is acute. The companion value √((1 − cosθ)/2) = 3/5 is sin(θ/2), 16/25 skips the square root, and 7/50 is the tempting but wrong 'halve the cosine'.