Question

f(x)=Acos^2(ωx+φ)+1(A>0,ω>0)的最大值为3,与y轴的焦点坐标为(0,2),其相邻两条对称轴之间

Answer 1

f(x)= Acos^2(ωx+φ)+1 = (A/2) cos(2ωx+2φ) + A/2 + 1 的最大值为3

=> A+1 = 3 => A=2

x=0, y = cos(2φ) + 2 = 2 => cos(2φ) =0

其相邻两条对称轴之间的距离为 2 => ω = π/2

=> f(x) = cos(πx+2φ) + ...