PQ=(1+sinθ-cosθ,1+cosθ-sinθ)
则
|PQ|
=根号[(1+sinθ-cosθ)^2+(1+cosθ-sinθ)^2]
=根号[(1+sinθ-cosθ)^2+(1+cosθ-sinθ)^2]
=根号[(1+(sinθ-cosθ)^2+2(sinθ-cosθ)+1+(cosθ-sinθ)^2-2(sinθ-cosθ)]
=根号(2-sin2θ)
取值范围:[1,根号3]
则当θ=3π/4时.|PQ|取得最大值:根号3
2.
sin^2(α+β)+psin(α+β)*cos(α+β)+qcos^2(α+β)
=sin^2(α+β)+cos^2(α+β) +psin(α+β)*cos(α+β)+(q-1)cos^2(α+β)
=1+psin(α+β)*cos(α+β)+(q-1)cos^2(α+β)
=1+cos(α+β)[psin(α+β)+(q-1)cos(α+β)]
=1+根号(p^2+(q-1)^2)cos(α+β)sin(α+β+Φ)
tanΦ=(q-1)/p
3.
连接圆心到矩形与弧的交点.连线与矩形边(与半径重合)夹角为α,
则一条矩形边为:1*sinα
另一条为:cosα-sinα/根号3
则面积为:
sinα*(cosα-sinα/根号3)
=sin2α-sin^2α/根号3
=sin2α-sin^2α/根号3
=sin2α+cos2α/2根号3-1/2根号3