Question

函数f(x)=(√3sinx-cosx)sinx的周期为____:最大值为____.

Answer 1

f(x) = √3sin²x - sinx cosx

= √3 × (1 - cos(2x))/2 - (sin(2x))/2 (利用二倍角公式)

= √3/2 - (√3/2)cos(2x) - (1/2)sin(2x)

= √3/2 - sin(π/3) cos(2x) - cos(π/3) sin(2x)

= √3/2 - sin(π/3 + 2x) (利用两角和的正弦公式)

周期 = 2π / 2 = π,最大值是√3/2+ 1.