Question

求函数y=sin^2(11π+x)-2sin(π/2-x)的最小值及相应的x值帮一下忙吧

Answer 1

y=(sin(11π+x))^2-2sin(π/2-x)
= (sinx)^2-2cosx=1-(cosx)^2-2cosx=2-(cosx+1)^2≥2-(1+1)^2=-2
y的最小值为-2，相应的x为x=2kπ, (k为整数）

Answer 2

y=(sin(11π+x))^2-2sin(π/2-x)
= (sinx)^2-2cosx
y' = 2sinxcosx +2sinx =0
2sinx(cosx+1)=0
sinx =0 or cosx =-1
y''(0) >0 min
min y at x=0
= 0-2 =-2