Question

当X属于[6分之派,7派/6]时,求函数y=3-sinx-2cos平方x的最小值和最大值?

Answer 1

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