三角函數(shù)sinα的值域是[-1,1]
1.y=sinx-√3cosx =2[(1/2)sinx - (√3/2)cosx] =2sin(x - π/3)
函數(shù)的最大值是2 ,函數(shù)的最小值是-2
∵當三角函數(shù)sinα=1時,α=2kπ + π/2 ,(k∈Z)
∴當函數(shù)y取最大值2時,x - π/3 = 2kπ + π/2 ,(k∈Z)
即：當x=2kπ + 5π/6 ,(k∈Z)時,ymax=2
∵當三角函數(shù)sinα=-1時,α=2kπ - π/2 ,(k∈Z)
∴當函數(shù)y取最小值-2時,x - π/3 = 2kπ - π/2 ,(k∈Z)
即：當x=2kπ - π/6 ,(k∈Z)時,ymin=-2
同理：2.y=sinx+cosx = √2[(√2/2)sinx + (√2/2)cosx]= √2sin(x + π/4)
函數(shù)的最大值是√2 ,函數(shù)的最小值是-√2
當x=2kπ + π/4 ,(k∈Z)時,ymax=√2
當x=2kπ - 3π/4 ,(k∈Z)時,ymin=-√2