当x∈[π/6,7π/6]时.函数y=3-sinx-2cos平方2;x的最小值,最大值

题目

当x∈[π/6,7π/6]时.函数y=3-sinx-2cos平方2;x的最小值,最大值

答案

y=3-sin x-2cos^2 x
=3-sin x-2+2sin^2 x
=2sin^2 x-sin x+1
=2(sin x-1/2)^2+1/2
X=[π/6,7π/6]
sinx=[-1/2,1]
所以
ymin=1/2
ymax=5/2