Question

函数y=sinxcosx和y=sinx+cosx的值域

Answer 1

y=sinxcosx
=1/2*sin2x
所以值域是[-1/2,1/2]

y=sinx+cosx
=√2(√2/2*sinx+√2/2cosx)
=√2(sinxcosπ/4+cosxsinπ/4)
=√2sin(x+π/4)
所以值域是[-√2,√2]

Answer 2

y=sinxcosx
=(2sinxcosx)/2
=sin2x/2
值域为：[-1/2，1/2]

y=sinx+cosx
=√2[(√2/2)sinx+(√2/2)cosx]
=√2[sinxcos(π/4)+cosxsin(π/4)]
=√2sin(x+π/4)
值域为：[-√2，√2]

Answer 3

解答：
y=sinxcosx=(1/2)sin2x
∴ 值域是[-1/2,1/2]
y=sinx+cosx
=√2[(√2/2)sinx+(√2/2)cosx]
=√2[sinxcos(π/4)+cosxsin(π/4)]
=√2sin(x+π/4)
∴ 值域为[-√2，√2]