y=1/2乘sinx^2+1/2sinxcosx+1麻烦化简一下.求T麻烦再求下φ好吗?

Question

y=1/2乘sinx^2+1/2sinxcosx+1
麻烦化简一下.求T
麻烦再求下φ好吗?

Answer 1

sinx^2 =(1-cos2x)/2
y=1/2*sinx^2+1/2sinxcosx+1
=1/2*(1-cos2x)/2+1/2*sin2x/2+1
=1/4-cos2x/4+sin2x/4+1
=sin2x/4-cos2x/4+5/4
=√2/4*(√2/2sin2x-√2/2cos2x)+5/4
=√2/4*(sin2xcosπ/4-cos2xsinπ/4)+5/4
=√2/4*sin(2x-π/4)+5/4
T=2π/2=π