If cos2θ = 1/9 and θ is acute, then sinθ equals:

Use the form cos2θ = 1 − 2si$n^2$θ: 1 − 2si$n^2$θ = 1/9 gives si$n^2$θ = 4/9, so sinθ = 2/3 for an acute angle. Check: sinθ = 2/3 means θ ≈ 41.8°, and cos83.6° ≈ 0.111 = 1/9. Reaching for cos2θ = 2co$s^2$θ − 1 instead answers cosθ = √5/3, forgetting the square root leaves 4/9, and simply halving the given number gives 1/3.