大师作文网求y=(sinx+2)(cosx+2)的值域
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求y=(sinx+2)(cosx+2)的值域
求y=(sinx+2)乘以(cosx+2)的值域
求y=(sinx+2)乘以(cosx+2)的值域
y=(sinx+2)(cosx+2)=sinxcosx+2(sinx+cosx)+4
=1/2sin2x+2√2sin(x+π/4)+4
=-1/2cos(2x+π/2)+2√2sin(x+π/4)+4
=-1/2(1-2sin(x+π/4)^2)+2√2sin(x+π/4)+4
=sin(x+π/4)^2+2√2sin(x+π/4)+7/2
=[sin(x+π/4)+√2]^2+3/2
则值域为[9/2-2√2,9/2+2√2]
=1/2sin2x+2√2sin(x+π/4)+4
=-1/2cos(2x+π/2)+2√2sin(x+π/4)+4
=-1/2(1-2sin(x+π/4)^2)+2√2sin(x+π/4)+4
=sin(x+π/4)^2+2√2sin(x+π/4)+7/2
=[sin(x+π/4)+√2]^2+3/2
则值域为[9/2-2√2,9/2+2√2]