if cos 2theta=1/3 and 0 less than or equal to 2theta less than or equal to pi, find cos theta

Answer 1

since 0 <= 2θ <= π,
0 <= θ <= π/2
That is, θ is in QI.

cos2θ = 2cos^2θ-1
so cosθ = √((1+cos2θ)/2) = √((1+1/3)/2) = √(2/3)
In the first quadrant, we don't have to worry about ± signs.