Question

求函数y=cos(x+π/3)-sim(x+π/3)的最大值,最小值和周期

Answer 1

y = cos(x+π/3) - sin(x+π/3)
= cos(x+π/3) - cos{π/2-(x+π/3)}
= cos(x+π/3) - cos(π/6-x)
= -2 sin{[(x+π/3)+(π/6-x)]/2} sin{[(x+π/3)-(π/6-x)]/2}
= -2sin(π/4) sin(x+π/12)
= -√2 sin(x+π/12)
-1 ≤ sin(x+π/12) ≤1
√2 ≥ -√2 sin(x+π/12) ≥ -√2
最大值√2，最小值-√2
最小正周期 = 2π/1 = 2π

Answer 2

y=sqrt(2){sin45*cos(x+π/3)-cos(45)*sim(x+π/3)}
=sqrt(2)sin(π/3-x-π/3)
所以最大值为根号2
最小值为负的根号2
周期还是2π

Answer 3

y=√2{sin45º*cos(x+π/3)-cos45º*sin(x+π/3)}
=√2sin(π/4-x-π/3)=-√2sin(x+π/12)
所以最大值为√2
最小值为-√2
周期还是2π