311×sin(314t)+62×cos(314t)
=[√(311^2+62^2)]×{[311/√(311^2+62^2)]×sin(314t)+[62/√(311^2+62^2)]×cos(314t)}
可见：[311/√(311^2+62^2)]^2+[62/√(311^2+62^2)]^2=1
不妨令：sinα=62/√(311^2+62^2),则：cosα=311/√(311^2+62^2),
代入上式,有：
311×sin(314t)+62×cos(314t)
=[√(311^2+62^2)]×[cosαsin(314t)+sinαcos(314t)]
=(√100565)×cosαsin(314t+α)
可见,所求信号的有效值是：√100565.