求函数值域 y=sinx+cosx如何推出y=根号2×sin(x+π/4)

问题描述:

求函数值域 y=sinx+cosx如何推出y=根号2×sin(x+π/4)

y=sinx+cosx
=√2*(√2/2sinx+√2/2cosx)
=√2*[sinxcos(π/4)+sin(π/4)cosx]
=√2*sin(x+π/4)