y=sin2次方x+2sinxcosx+3cos2次方x

y=sin2次方x+2sinxcosx+3cos2次方x
y=sin2次方x+2sinxcosx+3cos2次方x

y=sin2次方x+2sinxcosx+3cos2次方x
y=sin²x+2sinxcosx+3cos²x
=sin²x+cos²x+2sinxcosx+2cos²x
=1+2cos²x+sin2x
=cos2x+sin2x
=√2sin(2x+π/4)

y=sin2x+cos2x+2 =(根号2)sin(2x+派/4)+2 1.T=2派/2=派 2.值域【2-根号2，2+根号2】 3.由y=sinx的图像纵坐标不变，横坐标变为原来的1/

y=sin²x+2sinxcosx+3cos²x
=sin²x+cos²x+2sinxcosx+2cos²x
=1+sin2x+1+cos2x
=2+√2sin(2x+π/4)